The physics of spreading processes in multilayer networks
Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and func...
Saved in:
| Published in | Nature physics Vol. 12; no. 10; pp. 901 - 906 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Nature Publishing Group UK
01.10.2016
Nature Publishing Group |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1745-2473 1745-2481 |
| DOI | 10.1038/nphys3865 |
Cover
Loading…
| Abstract | Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.
Reshaping network theory to describe the multilayered structures of the real world has formed a focus in complex networks research in recent years. Progress in our understanding of dynamical processes is but one of the fruits of this labour. |
|---|---|
| AbstractList | Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include dierent types of relationships (or multiplexity) between their components. Such structural complexity has a signicant eect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple dierent structural relationships by encoding them in a convenient mathematical object. It also allows one to couple dierent dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or 'multiplexity') between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent multilayer approach for modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. Reshaping network theory to describe the multilayered structures of the real world has formed a focus in complex networks research in recent years. Progress in our understanding of dynamical processes is but one of the fruits of this labour. |
| Author | Porter, Mason A. Granell, Clara De Domenico, Manlio Arenas, Alex |
| Author_xml | – sequence: 1 givenname: Manlio orcidid: 0000-0001-5158-8594 surname: De Domenico fullname: De Domenico, Manlio email: manlio.dedomenico@urv.cat organization: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili – sequence: 2 givenname: Clara surname: Granell fullname: Granell, Clara organization: Department of Mathematics, Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina – sequence: 3 givenname: Mason A. surname: Porter fullname: Porter, Mason A. organization: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, CABDyN Complexity Centre, University of Oxford, Department of Mathematics, University of California – sequence: 4 givenname: Alex orcidid: 0000-0003-0937-0334 surname: Arenas fullname: Arenas, Alex email: alexandre.arenas@urv.cat organization: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili |
| BookMark | eNptkN9KwzAUh4NMcJte-AYFb1SoS5om6byT4T8YeDOvS5KeuswuqUmL7G18Fp_MjInIFAInF9_v8DvfCA2ss4DQKcFXBNNiYtvlJtCCswM0JCJnaZYXZPDzF_QIjUJYYZxnnNAhul4sIdlmjA6Jq5PQepCVsS9J652GECAkxibrvulMIzfgPz8sdO_Ov4ZjdFjLJsDJ9xyj57vbxewhnT_dP85u5qmmU9KlCldc6EqqDHIMICrGKipgyqWoua6yuhJTIUGAIlgxrZgAzaikVOFMKSLoGJ3v9sZGbz2ErlyboKFppAXXh5IUOSswjxdF9GwPXbne29guUhljvKDxjdFkR2nvQvBQl9p0sjPOdl6apiS43Losf1zGxMVeovVmLf3mX_Zyx0aV0SP4Xx3-wF9tjYgE |
| CitedBy_id | crossref_primary_10_1038_s41598_020_75147_w crossref_primary_10_1038_s41467_018_08009_9 crossref_primary_10_1109_TCYB_2020_3006032 crossref_primary_10_1137_19M1257123 crossref_primary_10_3390_e24081147 crossref_primary_10_1063_1_5121394 crossref_primary_10_1016_j_neuroimage_2021_118705 crossref_primary_10_1063_5_0023427 crossref_primary_10_1063_1_5010766 crossref_primary_10_1063_5_0126799 crossref_primary_10_1109_TVT_2024_3440958 crossref_primary_10_1186_s12859_019_2800_y crossref_primary_10_1209_0295_5075_129_10002 crossref_primary_10_1209_0295_5075_133_48003 crossref_primary_10_1016_j_tics_2017_06_009 crossref_primary_10_1103_PhysRevX_10_021069 crossref_primary_10_1007_s11229_022_04008_y crossref_primary_10_1109_TCSI_2021_3050988 crossref_primary_10_1038_s42254_023_00676_y crossref_primary_10_1088_1367_2630_ab023e crossref_primary_10_1016_j_physa_2022_127209 crossref_primary_10_1038_s41598_018_20864_6 crossref_primary_10_1016_j_matcom_2021_04_017 crossref_primary_10_1103_PhysRevE_104_024309 crossref_primary_10_1103_PhysRevResearch_5_033065 crossref_primary_10_1103_PhysRevResearch_2_033005 crossref_primary_10_1103_PhysRevE_104_024302 crossref_primary_10_1140_epjds_s13688_020_00233_y crossref_primary_10_3390_w11020246 crossref_primary_10_1103_PhysRevE_104_034311 crossref_primary_10_1109_ACCESS_2025_3539345 crossref_primary_10_1093_gigascience_gix004 crossref_primary_10_1016_j_neunet_2022_02_023 crossref_primary_10_1073_pnas_2302245120 crossref_primary_10_1063_1_4990592 crossref_primary_10_1109_TNNLS_2023_3341347 crossref_primary_10_1142_S0219525917500151 crossref_primary_10_1146_annurev_phyto_080516_035326 crossref_primary_10_1007_s41109_023_00572_5 crossref_primary_10_1038_s41467_023_37323_0 crossref_primary_10_1073_pnas_1604405114 crossref_primary_10_1142_S0218202521500536 crossref_primary_10_1016_j_chaos_2017_11_008 crossref_primary_10_1088_1367_2630_ab461c crossref_primary_10_1088_1742_5468_ab6a04 crossref_primary_10_1016_j_physa_2022_128439 crossref_primary_10_21105_joss_05116 crossref_primary_10_1016_j_physleta_2019_125996 crossref_primary_10_1103_PhysRevE_104_024402 crossref_primary_10_1109_TCNS_2019_2903907 crossref_primary_10_3390_math10040588 crossref_primary_10_1038_s41567_019_0459_y crossref_primary_10_1088_1742_5468_abd310 crossref_primary_10_1103_PhysRevResearch_3_L032045 crossref_primary_10_1063_5_0042155 crossref_primary_10_1063_5_0044327 crossref_primary_10_1063_5_0004826 crossref_primary_10_1063_1_4985185 crossref_primary_10_1016_j_physrep_2019_07_001 crossref_primary_10_1016_j_plrev_2019_07_003 crossref_primary_10_1098_rstb_2019_0498 crossref_primary_10_1103_PhysRevE_100_022316 crossref_primary_10_1007_s11431_021_1977_3 crossref_primary_10_1038_s41467_021_25485_8 crossref_primary_10_1016_j_chaos_2019_109548 crossref_primary_10_1016_j_physa_2019_04_143 crossref_primary_10_1103_PhysRevX_8_031038 crossref_primary_10_1007_s10955_017_1858_z crossref_primary_10_1103_PhysRevX_8_031039 crossref_primary_10_1155_2021_9923837 crossref_primary_10_1109_TCYB_2024_3367783 crossref_primary_10_1007_s11071_023_08542_3 crossref_primary_10_1007_s41745_019_0103_y crossref_primary_10_1371_journal_pone_0279345 crossref_primary_10_1016_j_physleta_2024_129772 crossref_primary_10_1063_5_0205793 crossref_primary_10_3390_a14070189 crossref_primary_10_1137_18M1231304 crossref_primary_10_1109_ACCESS_2020_2965547 crossref_primary_10_1371_journal_pone_0245396 crossref_primary_10_1038_s41598_021_87987_1 crossref_primary_10_1038_s41598_017_01655_x crossref_primary_10_1142_S0217979218503095 crossref_primary_10_1098_rsta_2020_0410 crossref_primary_10_1103_PhysRevE_102_052304 crossref_primary_10_1109_TMC_2019_2923665 crossref_primary_10_1109_TNSE_2022_3186159 crossref_primary_10_1007_s41109_021_00402_6 crossref_primary_10_1038_s41598_020_79507_4 crossref_primary_10_1371_journal_pcsy_0000033 crossref_primary_10_1016_j_joi_2024_101591 crossref_primary_10_1038_s41562_020_00994_6 crossref_primary_10_1038_s44284_024_00188_5 crossref_primary_10_1137_21M1406180 crossref_primary_10_1109_TNSE_2022_3208343 crossref_primary_10_1063_1_5039483 crossref_primary_10_15407_fm29_03_419 crossref_primary_10_1007_s41109_020_00310_1 crossref_primary_10_1007_s41109_024_00632_4 crossref_primary_10_1109_ACCESS_2020_2975357 crossref_primary_10_1016_j_physleta_2024_129673 crossref_primary_10_3390_mca26040068 crossref_primary_10_1016_j_physa_2018_02_157 crossref_primary_10_1103_PhysRevE_107_024309 crossref_primary_10_1109_JIOT_2023_3294470 crossref_primary_10_1038_s42254_018_0002_6 crossref_primary_10_1016_j_physa_2019_122028 crossref_primary_10_1016_j_physa_2019_04_214 crossref_primary_10_1080_00018732_2019_1650450 crossref_primary_10_1038_s42005_019_0152_6 crossref_primary_10_1209_0295_5075_130_48002 crossref_primary_10_1103_PhysRevE_99_012308 crossref_primary_10_1063_1_5077075 crossref_primary_10_1371_journal_pcbi_1012678 crossref_primary_10_1103_PhysRevE_99_012312 crossref_primary_10_1016_j_chaos_2020_110621 crossref_primary_10_1016_j_eswa_2024_126042 crossref_primary_10_1209_0295_5075_124_58004 crossref_primary_10_1109_TCCN_2020_3027697 crossref_primary_10_1016_j_neuroimage_2024_120582 crossref_primary_10_1103_PhysRevE_95_052312 crossref_primary_10_1016_j_plrev_2017_12_006 crossref_primary_10_3389_fpsyg_2021_623970 crossref_primary_10_1109_ACCESS_2022_3160206 crossref_primary_10_1103_PhysRevE_99_012302 crossref_primary_10_1103_PhysRevResearch_5_033220 crossref_primary_10_1016_j_physa_2017_11_099 crossref_primary_10_1103_PhysRevE_105_064301 crossref_primary_10_1016_j_physleta_2024_130159 crossref_primary_10_1007_s13278_024_01331_9 crossref_primary_10_1063_5_0161399 crossref_primary_10_1109_ACCESS_2021_3090997 crossref_primary_10_1038_s41598_019_52326_y crossref_primary_10_1038_s41598_019_38869_0 crossref_primary_10_1140_epjb_s10051_024_00693_5 crossref_primary_10_1007_s41109_020_00301_2 crossref_primary_10_3389_fict_2017_00022 crossref_primary_10_1016_j_jhydrol_2024_132604 crossref_primary_10_1093_bioinformatics_btx252 crossref_primary_10_1016_j_physa_2020_125410 crossref_primary_10_1103_PhysRevX_14_021007 crossref_primary_10_1103_PhysRevE_101_052309 crossref_primary_10_1109_TSMC_2018_2882782 crossref_primary_10_1109_TNSE_2019_2894142 crossref_primary_10_1016_j_ins_2018_08_050 crossref_primary_10_1103_PhysRevE_103_022320 crossref_primary_10_1007_s11071_020_06021_7 crossref_primary_10_1103_PhysRevE_95_062215 crossref_primary_10_1016_j_physa_2018_02_115 crossref_primary_10_1038_s41598_018_20730_5 crossref_primary_10_1038_s41598_017_07591_0 crossref_primary_10_1016_j_chaos_2022_112447 crossref_primary_10_1073_pnas_1920986117 crossref_primary_10_1142_S0219720020500201 crossref_primary_10_1109_TNSE_2020_2968436 crossref_primary_10_1038_s42005_021_00695_0 crossref_primary_10_1038_s42005_023_01369_9 crossref_primary_10_1109_TCYB_2018_2853611 crossref_primary_10_1038_s41567_021_01371_4 crossref_primary_10_1016_j_physa_2018_11_045 crossref_primary_10_3390_pr8030312 crossref_primary_10_1103_PhysRevE_97_060301 crossref_primary_10_1038_srep46730 crossref_primary_10_1002_wics_1566 crossref_primary_10_3390_math11071573 crossref_primary_10_1088_1367_2630_aaf660 crossref_primary_10_1016_j_amc_2018_12_045 crossref_primary_10_1016_j_neucom_2018_05_109 crossref_primary_10_1103_PhysRevResearch_3_013157 crossref_primary_10_1007_s00265_022_03218_1 crossref_primary_10_1109_ACCESS_2021_3116868 crossref_primary_10_1103_PhysRevE_100_020301 crossref_primary_10_1109_TCSS_2024_3396229 crossref_primary_10_1088_1742_5468_aa5fd8 crossref_primary_10_1016_j_jfranklin_2023_03_032 crossref_primary_10_1063_5_0165796 crossref_primary_10_1109_TCYB_2019_2960605 crossref_primary_10_2139_ssrn_4173672 crossref_primary_10_1093_comnet_cnz027 crossref_primary_10_3389_fphy_2021_755567 crossref_primary_10_1038_s41598_024_69354_y crossref_primary_10_1016_j_envsoft_2018_08_002 crossref_primary_10_1016_j_comnet_2023_109747 crossref_primary_10_1038_s41567_023_02132_1 crossref_primary_10_3390_e25030471 crossref_primary_10_1063_1_5121401 crossref_primary_10_1063_5_0092464 crossref_primary_10_1111_2041_210X_13655 crossref_primary_10_1016_j_isci_2023_106181 crossref_primary_10_1103_PhysRevE_96_062309 crossref_primary_10_1016_j_plrev_2017_11_003 crossref_primary_10_1140_epjb_e2016_70248_6 crossref_primary_10_1137_19M1254040 crossref_primary_10_1016_j_physrep_2023_03_005 crossref_primary_10_1109_TNSE_2017_2775152 crossref_primary_10_1002_adma_202416988 crossref_primary_10_3390_e25030458 crossref_primary_10_1016_j_tree_2018_03_008 crossref_primary_10_1016_j_chaos_2025_116238 crossref_primary_10_1063_1_5063960 crossref_primary_10_1088_1367_2630_abdb71 crossref_primary_10_1093_cercor_bhab357 crossref_primary_10_1109_TCSS_2022_3161305 crossref_primary_10_1038_s41598_019_49173_2 crossref_primary_10_1093_comnet_cnab032 crossref_primary_10_1137_21M1457321 crossref_primary_10_3390_sym11020284 crossref_primary_10_1140_epjb_e2017_80122_8 crossref_primary_10_1038_s41598_018_37942_4 crossref_primary_10_1109_TSMC_2019_2960156 crossref_primary_10_1038_ni_3727 crossref_primary_10_1063_1_5017962 crossref_primary_10_1088_1742_5468_aabfcc crossref_primary_10_1088_1367_2630_aad723 crossref_primary_10_1089_big_2019_0169 crossref_primary_10_1142_S0129626424500117 crossref_primary_10_1103_PhysRevE_107_044304 crossref_primary_10_1016_j_chaos_2024_115914 crossref_primary_10_1016_j_chaos_2023_113229 crossref_primary_10_1016_j_anbehav_2018_12_016 crossref_primary_10_1093_comnet_cnx050 crossref_primary_10_1140_epjds_s13688_018_0139_7 crossref_primary_10_1063_1_5093047 crossref_primary_10_1140_epjb_s10051_024_00722_3 crossref_primary_10_1073_pnas_1904421116 crossref_primary_10_1162_netn_a_00033 crossref_primary_10_1088_1367_2630_abe0db crossref_primary_10_3389_fnhum_2022_848026 crossref_primary_10_7554_eLife_68531 crossref_primary_10_1103_PhysRevE_100_052312 crossref_primary_10_1140_epjds_s13688_018_0180_6 crossref_primary_10_1038_s41467_020_19024_0 crossref_primary_10_1016_j_physa_2019_121355 crossref_primary_10_1038_s41598_021_02418_5 crossref_primary_10_1093_comnet_cnx042 crossref_primary_10_1007_s00332_017_9436_8 crossref_primary_10_1093_comnet_cnx041 crossref_primary_10_1038_s41598_018_20105_w crossref_primary_10_1038_s42254_020_00264_4 crossref_primary_10_1007_s00285_022_01810_7 crossref_primary_10_1063_1_5108951 crossref_primary_10_3934_era_2022193 crossref_primary_10_1007_s42001_025_00364_0 crossref_primary_10_1038_s41467_019_10063_w crossref_primary_10_1016_j_iot_2020_100312 crossref_primary_10_1155_2020_5409401 crossref_primary_10_3390_su12020746 crossref_primary_10_1111_ele_12898 crossref_primary_10_1109_TCSS_2019_2909269 crossref_primary_10_1155_2020_2363514 crossref_primary_10_15407_kvt208_02_082 crossref_primary_10_1038_s41467_017_01442_2 crossref_primary_10_1016_j_nicl_2023_103428 crossref_primary_10_1016_j_jfranklin_2018_07_040 crossref_primary_10_1016_j_ins_2022_11_033 crossref_primary_10_3390_a10010001 crossref_primary_10_1103_PhysRevE_98_012302 crossref_primary_10_1109_TNSE_2023_3243560 crossref_primary_10_1088_1742_5468_ab5700 crossref_primary_10_1371_journal_pone_0252266 crossref_primary_10_1038_s42005_021_00634_z crossref_primary_10_1088_1367_2630_aaf3ea crossref_primary_10_1016_j_strueco_2023_07_006 crossref_primary_10_1088_2632_072X_ad0e23 crossref_primary_10_1088_1367_2630_ab8e5e crossref_primary_10_1016_j_physa_2024_129832 crossref_primary_10_1088_1367_2630_ab060c crossref_primary_10_1088_1367_2630_ab060f crossref_primary_10_1103_PhysRevE_104_054305 crossref_primary_10_1137_20M1355896 crossref_primary_10_1103_PhysRevE_102_022310 crossref_primary_10_1103_PhysRevE_96_042312 crossref_primary_10_3934_mbe_2023024 crossref_primary_10_3389_fphy_2022_1017015 crossref_primary_10_1098_rspa_2022_0059 crossref_primary_10_1016_j_chaos_2020_110545 crossref_primary_10_1209_0295_5075_121_48006 crossref_primary_10_1007_s41109_021_00366_7 crossref_primary_10_1155_2019_6159365 crossref_primary_10_1088_1367_2630_ab32c7 crossref_primary_10_1109_ACCESS_2019_2904623 crossref_primary_10_1103_PhysRevE_106_024214 crossref_primary_10_55648_1998_6920_2024_18_3_45_56 crossref_primary_10_1163_1568539X_00003493 crossref_primary_10_1209_0295_5075_130_30007 crossref_primary_10_1103_PhysRevE_98_032104 crossref_primary_10_1016_j_physrep_2020_05_004 crossref_primary_10_1103_PhysRevLett_118_168301 crossref_primary_10_1016_j_physa_2021_126457 crossref_primary_10_1103_PhysRevE_96_042302 crossref_primary_10_1016_j_eswa_2022_117525 crossref_primary_10_1016_j_physleta_2024_130199 crossref_primary_10_1038_s42005_022_01039_2 crossref_primary_10_1109_ACCESS_2020_3031014 crossref_primary_10_1016_j_physa_2020_125184 crossref_primary_10_1088_1367_2630_acd020 crossref_primary_10_1103_PhysRevResearch_2_023176 crossref_primary_10_1007_s11227_024_06404_2 crossref_primary_10_1155_2022_9873569 crossref_primary_10_1063_1_5090902 crossref_primary_10_1038_s41746_024_01402_3 crossref_primary_10_1016_j_physa_2017_12_081 crossref_primary_10_1016_j_physa_2023_129297 crossref_primary_10_3389_fnhum_2024_1416667 crossref_primary_10_1098_rspa_2019_0825 crossref_primary_10_1109_TCYB_2019_2915664 crossref_primary_10_1109_ACCESS_2024_3407832 crossref_primary_10_3390_sym11060763 crossref_primary_10_1103_PhysRevX_6_041062 crossref_primary_10_1038_s42005_021_00631_2 crossref_primary_10_1103_PhysRevResearch_2_013155 crossref_primary_10_1209_0295_5075_125_18003 crossref_primary_10_1140_epjst_e2019_800203_3 crossref_primary_10_1016_j_chaos_2022_112921 crossref_primary_10_1038_s41598_018_21054_0 crossref_primary_10_1103_PhysRevResearch_5_013196 crossref_primary_10_1038_s41540_019_0092_5 crossref_primary_10_1016_j_neuron_2017_11_007 crossref_primary_10_1016_j_sleep_2024_02_013 crossref_primary_10_1016_j_knosys_2021_107365 crossref_primary_10_3390_e25121615 crossref_primary_10_1063_5_0232563 crossref_primary_10_1088_1742_5468_abffcb crossref_primary_10_3390_app122111216 crossref_primary_10_1016_j_chaos_2021_111200 crossref_primary_10_1093_bib_bbab080 crossref_primary_10_15407_fm29_04_586 crossref_primary_10_1103_PhysRevResearch_5_013084 crossref_primary_10_1007_s10618_020_00716_6 crossref_primary_10_1038_s42005_025_01940_6 crossref_primary_10_1016_j_physa_2024_129906 crossref_primary_10_1146_annurev_conmatphys_031218_013259 crossref_primary_10_1088_1751_8121_ab766b crossref_primary_10_1140_epjb_e2020_100075_1 crossref_primary_10_1209_0295_5075_129_30004 crossref_primary_10_1109_TCNS_2022_3203352 crossref_primary_10_1145_3627816 crossref_primary_10_1088_1742_5468_ab780e crossref_primary_10_1109_TNSE_2017_2753963 crossref_primary_10_1103_PhysRevE_94_062308 crossref_primary_10_1142_S0129183124500414 crossref_primary_10_1002_adma_202311040 crossref_primary_10_1103_PhysRevResearch_2_023259 crossref_primary_10_1103_PhysRevE_98_062303 crossref_primary_10_1002_adma_202403904 crossref_primary_10_1103_PhysRevE_105_044126 crossref_primary_10_1007_s00248_022_02108_3 crossref_primary_10_1103_PhysRevE_103_042301 crossref_primary_10_1038_s41467_019_11763_z crossref_primary_10_1155_2021_8643873 crossref_primary_10_1016_j_physa_2019_03_068 crossref_primary_10_1109_TCSI_2019_2955972 crossref_primary_10_1038_s42254_022_00483_x crossref_primary_10_1140_epjst_e2019_900052_3 crossref_primary_10_1016_j_cnsns_2020_105403 crossref_primary_10_1016_j_amc_2025_129328 crossref_primary_10_1016_j_chaos_2021_110692 crossref_primary_10_1103_PhysRevE_95_012312 crossref_primary_10_1016_j_chaos_2023_114296 crossref_primary_10_1021_acs_analchem_4c02183 crossref_primary_10_1177_23998083221108190 crossref_primary_10_1093_texcom_tgac024 crossref_primary_10_1103_PhysRevX_7_011013 crossref_primary_10_1016_j_physa_2021_126238 crossref_primary_10_1063_5_0091626 crossref_primary_10_3390_brainsci10120915 crossref_primary_10_1016_j_automatica_2022_110185 crossref_primary_10_1016_j_physrep_2025_01_006 crossref_primary_10_1017_nws_2016_22 crossref_primary_10_1063_5_0054770 crossref_primary_10_1103_PhysRevE_97_022311 crossref_primary_10_3390_math8111895 crossref_primary_10_1016_j_physrep_2024_01_003 crossref_primary_10_1209_0295_5075_125_10009 crossref_primary_10_1016_j_physrep_2017_07_007 crossref_primary_10_1103_PhysRevE_97_042314 crossref_primary_10_1103_PhysRevE_98_062321 crossref_primary_10_1140_epjst_e2019_900051_9 crossref_primary_10_1088_1402_4896_adb9a2 crossref_primary_10_1109_LCSYS_2023_3280116 crossref_primary_10_1007_s12652_023_04589_7 crossref_primary_10_1016_j_physa_2018_09_075 crossref_primary_10_1088_1367_2630_aac0c9 crossref_primary_10_1109_ACCESS_2019_2902856 crossref_primary_10_1088_1367_2630_aa9cda crossref_primary_10_7717_peerj_14571 crossref_primary_10_3389_fvets_2020_00596 crossref_primary_10_1109_TNSE_2018_2871726 crossref_primary_10_1103_PhysRevResearch_2_033164 crossref_primary_10_1103_PhysRevResearch_6_013136 crossref_primary_10_1038_s41598_022_07249_6 crossref_primary_10_1103_PhysRevE_101_022308 crossref_primary_10_1109_OJCOMS_2024_3393848 crossref_primary_10_1140_epjst_e2018_800037_y crossref_primary_10_1088_2632_072X_ad7f16 crossref_primary_10_1109_JSTSP_2018_2844813 crossref_primary_10_1109_ACCESS_2022_3168659 crossref_primary_10_3390_fi13050135 crossref_primary_10_1093_cz_zoaa079 crossref_primary_10_1103_PhysRevE_98_052305 crossref_primary_10_7554_eLife_32814 crossref_primary_10_1016_j_chaos_2023_114246 crossref_primary_10_1155_2021_6687463 crossref_primary_10_1016_j_conb_2022_102532 crossref_primary_10_1016_j_firesaf_2024_104250 crossref_primary_10_1142_S0129183119500827 crossref_primary_10_3389_fphy_2017_00011 crossref_primary_10_1007_s10329_018_0686_3 crossref_primary_10_1080_09720529_2019_1582870 crossref_primary_10_1038_s41467_017_00587_4 crossref_primary_10_1016_j_neucom_2019_10_011 crossref_primary_10_1103_PhysRevE_98_052315 crossref_primary_10_1016_j_chaos_2020_110477 crossref_primary_10_1088_2632_072X_abe6e9 crossref_primary_10_1016_j_chaos_2023_113166 crossref_primary_10_1007_s10473_019_0618_3 crossref_primary_10_1016_j_physa_2024_130196 crossref_primary_10_1063_5_0008341 crossref_primary_10_3390_e25121610 crossref_primary_10_1103_PhysRevE_97_032308 crossref_primary_10_1103_PhysRevE_97_032307 crossref_primary_10_1140_epjds_s13688_020_00258_3 crossref_primary_10_1103_PhysRevResearch_2_013312 crossref_primary_10_1088_2632_072X_ac457a crossref_primary_10_1016_j_patcog_2019_06_009 crossref_primary_10_1103_PhysRevX_11_021059 crossref_primary_10_1088_1742_5468_ac9617 crossref_primary_10_1016_j_cjph_2024_10_017 crossref_primary_10_1142_S0217979221501794 crossref_primary_10_1007_s11071_023_08793_0 |
| Cites_doi | 10.1103/PhysRevE.89.032804 10.1038/srep10650 10.1137/07070111X 10.1038/nphys2761 10.1007/978-3-319-26641-1 10.1103/PhysRevLett.114.038701 10.1038/nature08932 10.1371/journal.pone.0086028 10.1103/PhysRevE.71.026125 10.1038/srep06911 10.1016/j.plrev.2015.07.006 10.1038/srep00620 10.1103/PhysRevE.92.032805 10.1371/journal.pone.0078293 10.1098/rsta.2015.0117 10.1209/epl/i2005-10080-8 10.1038/srep10840 10.1080/14697688.2014.968356 10.1103/PhysRevE.94.032908 10.1038/nphys3081 10.1103/PhysRevE.85.066109 10.1137/140976649 10.1103/PhysRevLett.109.128703 10.1038/nrn3214 10.1073/pnas.1318469111 10.1093/comnet/cnu016 10.1063/1.4818544 10.1103/PhysRevLett.110.028701 10.1103/PhysRevE.90.012808 10.1088/1367-2630/14/3/033035 10.1103/PhysRevE.87.062806 10.1109/TNSE.2015.2425961 10.1371/journal.pone.0097857 10.1103/PhysRevE.92.042807 10.1103/PhysRevLett.89.248701 10.1103/PhysRevLett.111.128701 10.1016/j.epidem.2014.09.005 10.1016/0378-8733(78)90011-4 10.1103/PhysRevE.90.042814 10.1016/j.physrep.2010.11.002 10.1103/PhysRevE.82.036106 10.1209/0295-5075/97/16006 10.1103/PhysRevLett.116.108701 10.1103/PhysRevE.92.032804 10.1093/acprof:oso/9780199206650.001.0001 10.1017/CBO9780511815478 10.1103/PhysRevE.88.050801 10.1103/PhysRevE.89.042811 10.1016/j.arcontrol.2014.09.003 10.1126/science.1184819 10.1073/pnas.1422487112 10.1103/PhysRevLett.109.248701 10.1016/j.physrep.2014.07.001 10.1140/epjb/e2015-50742-1 10.1038/ncomms7864 10.1103/PhysRevE.89.062813 10.1103/PhysRevE.88.032807 10.1126/sciadv.1500445 10.1126/science.1245200 10.1038/srep10073 10.1088/1367-2630/17/7/073029 10.1038/srep01344 10.1038/nphys2180 10.1016/j.physrep.2005.10.009 10.1140/epjb/e2015-60270-7 10.1073/pnas.0810762106 10.1137/130949191 10.1103/PhysRevE.89.062814 10.1038/ncomms7868 10.1137/15M1009615 |
| ContentType | Journal Article |
| Copyright | Springer Nature Limited 2016 Copyright Nature Publishing Group Oct 2016 |
| Copyright_xml | – notice: Springer Nature Limited 2016 – notice: Copyright Nature Publishing Group Oct 2016 |
| DBID | AAYXX CITATION 3V. 7U5 7XB 88I 8FD 8FE 8FG 8FK ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR CCPQU DWQXO GNUQQ HCIFZ L7M M2P P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI Q9U |
| DOI | 10.1038/nphys3865 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Solid State and Superconductivity Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection Advanced Technologies Database with Aerospace Science Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Central Student Technology Collection Technology Research Database ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central Earth, Atmospheric & Aquatic Science Collection ProQuest One Applied & Life Sciences ProQuest One Sustainability Natural Science Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Advanced Technologies & Aerospace Collection ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Solid State and Superconductivity Abstracts ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | ProQuest Central Student Technology Research Database |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1745-2481 |
| EndPage | 906 |
| ExternalDocumentID | 4202901291 10_1038_nphys3865 |
| Genre | Feature |
| GroupedDBID | 0R~ 123 29M 39C 3V. 4.4 5BI 5M7 6OB 70F 88I 8FE 8FG 8FH 8R4 8R5 AAEEF AARCD AAYZH AAZLF ABAWZ ABDBF ABJNI ABLJU ABUWG ABZEH ACBWK ACGFO ACGFS ACGOD ACMJI ACUHS ADBBV ADFRT AENEX AEUYN AFBBN AFKRA AFSHS AFWHJ AGAYW AGHTU AHBCP AHOSX AHSBF AIBTJ ALFFA ALMA_UNASSIGNED_HOLDINGS AMTXH ARAPS ARMCB ASPBG AVWKF AXYYD AZFZN AZQEC BENPR BGLVJ BHPHI BKKNO BKSAR BPHCQ CCPQU DB5 DU5 DWQXO EBS EE. EJD ESX EXGXG F5P FEDTE FQGFK FSGXE GNUQQ HCIFZ HVGLF HZ~ I-F LGEZI LK5 LOTEE M2P M7R N9A NADUK NNMJJ NXXTH O9- ODYON P2P P62 PCBAR PQQKQ PROAC Q2X RNS RNT RNTTT SHXYY SIXXV SJN SNYQT SOJ TAOOD TBHMF TDRGL TSG TUS ~8M AAYXX ACMFV ACSTC AFANA ALPWD ATHPR CITATION PHGZM PHGZT 7U5 7XB 8FD 8FK L7M PKEHL PQEST PQGLB PQUKI Q9U |
| ID | FETCH-LOGICAL-c391t-b0d67cdab2e40ee7d55d37e96a7f6cd2fd797ae7eb10b5cb57ec53a33b02bb173 |
| IEDL.DBID | BENPR |
| ISSN | 1745-2473 |
| IngestDate | Thu Jul 10 19:26:49 EDT 2025 Sat Aug 23 12:55:37 EDT 2025 Thu Apr 24 23:04:02 EDT 2025 Tue Jul 01 00:25:38 EDT 2025 Fri Feb 21 02:38:30 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c391t-b0d67cdab2e40ee7d55d37e96a7f6cd2fd797ae7eb10b5cb57ec53a33b02bb173 |
| Notes | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
| ORCID | 0000-0003-0937-0334 0000-0001-5158-8594 |
| PQID | 1825568368 |
| PQPubID | 27545 |
| PageCount | 6 |
| ParticipantIDs | proquest_miscellaneous_1845806042 proquest_journals_1825568368 crossref_citationtrail_10_1038_nphys3865 crossref_primary_10_1038_nphys3865 springer_journals_10_1038_nphys3865 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2016-10-01 |
| PublicationDateYYYYMMDD | 2016-10-01 |
| PublicationDate_xml | – month: 10 year: 2016 text: 2016-10-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London |
| PublicationTitle | Nature physics |
| PublicationTitleAbbrev | Nature Phys |
| PublicationYear | 2016 |
| Publisher | Nature Publishing Group UK Nature Publishing Group |
| Publisher_xml | – name: Nature Publishing Group UK – name: Nature Publishing Group |
| References | Sole-RibaltaASpectral properties of the Laplacian of multiplex networksPhys. Rev. E2013880328072013PhRvE..88c2807S10.1103/PhysRevE.88.032807 KrioukovDPapadopoulosFKitsakMVahdatABoguñáMHyperbolic geometry of complex networksPhys. Rev. E2010820361062010PhRvE..82c6106K278799810.1103/PhysRevE.82.036106 BuldyrevS VParshaniRPaulGStanleyH EHavlinSCatastrophic cascade of failures in interdependent networksNature2010464102510282010Natur.464.1025B10.1038/nature08932 Gómez-GardeñesJde DomenicoMGutiérrezGArenasAGómezSLayer–layer competition in multiplex complex networksPhil. Trans. R. Soc. A2015373201501172015RSPTA.37350117G10.1098/rsta.2015.0117 WangZAndrewsM AWuZ-XWangLBauchC TCoupled disease–behavior dynamics on complex networks: a reviewPhys. Life Rev.2015151292015PhLRv..15....1W10.1016/j.plrev.2015.07.006 SonS-WBizhaniGChristensenCGrassbergerPPaczuskiMPercolation theory on interdependent networks based on epidemic spreadingEurophys. Lett.201297160062012EL.....9716006S10.1209/0295-5075/97/16006 WassermanSFaustKSocial Network Analysis: Methods and Applications19940926.9106610.1017/CBO9780511815478 TangYQianFGaoHKurthsJSynchronization in complex networks and its application—a survey of recent advances and challengesAnnu. Rev. Control20143818419810.1016/j.arcontrol.2014.09.003 SalehiMSpreading processes in multilayer networksIEEE Trans. Netw. Sci. Eng.20152658310.1109/TNSE.2015.2425961 BrockmannDHelbingDThe hidden geometry of complex, network-driven contagion phenomenaScience2013342133713422013Sci...342.1337B10.1126/science.1245200 De DomenicoMNicosiaVArenasALatoraVStructural reducibility of multilayer networksNat. Commun.2015668642015NatCo...6.6864D10.1038/ncomms7864 Solé-RibaltaAGómezSArenasACongestion induced by the structure of multiplex networksPhys. Rev. Lett.20161161087012016PhRvL.116j8701S10.1103/PhysRevLett.116.108701 GallottiRPorterM ABarthelemyMLost in transportation: information measures and cognitive limits in multilayer navigationSci. Adv.20162e15004452016SciA....2E0445G10.1126/sciadv.1500445 De DomenicoMMathematical formulation of multi-layer networksPhys. Rev. X20133041022 BraunUDynamic reconfiguration of frontal brain networks during executive cognition in humansProc. Natl Acad. Sci. USA201511211678116832015PNAS..11211678B10.1073/pnas.1422487112 ZhaoLLaiY-CParkKYeNOnset of traffic congestion in complex networksPhys. Rev. E2005710261252005PhRvE..71b6125Z10.1103/PhysRevE.71.026125 BarthelemyMSpatial networksPhys. Rep.201149911012011PhR...499....1B277096210.1016/j.physrep.2010.11.002 GallottiRBarthelemyMAnatomy and efficiency of urban multimodal mobilitySci. Rep.2014469112014NatSR...4E6911G10.1038/srep06911 RadicchiFDriving interconnected networks to supercriticalityPhys. Rev. X20144021014 Aldous, D. & Fill, J. A. Reversible Markov Chains and Random Walks on Graphs Unfinished monograph, recompiled 2014 (2002); https://www.stat.berkeley.edu/∼aldous/RWG/book.html GranellCGómezSArenasACompeting spreading processes on multiplex networks: awareness and epidemicsPhys. Rev. E2014900128082014PhRvE..90a2808G10.1103/PhysRevE.90.012808 BianconiGStatistical mechanics of multiplex networks: entropy and overlapPhys. Rev. E2013870628062013PhRvE..87f2806B10.1103/PhysRevE.87.062806 CozzoEStructure of triadic relations in multiplex networksNew J. Phys.2015170730292015NJPh...17g3029C10.1088/1367-2630/17/7/073029 SolaLEigenvector centrality of nodes in multiplex networksChaos201330331312013Chaos..23c3131S1323.0511710.1063/1.4818544 BargigliLDi IasioGInfanteLLilloFPierobonFThe multiplex structure of interbank networksQuant. Financ.20151567369133210851398.9170310.1080/14697688.2014.968356 AbrahamIChechikSKempeDSlivkinsALow-distortion inference of latent similarities from a multiplex social networkSIAM J. Comput.20154461766833526201422.9160410.1137/130949191 BoccalettiSLatoraVMorenoYChavezMHwangD-UComplex networks: structure and dynamicsPhys. Rep.20064241753082006PhR...424..175B21936211371.8200210.1016/j.physrep.2005.10.009 LeeK-MMinBGohK-ITowards real-world complexity: an introduction to multiplex networksEur. Phys. J. B201588482015EPJB...88...48L10.1140/epjb/e2015-50742-1 GómezSDiffusion dynamics on multiplex networksPhys. Rev. Lett.20131100287012013PhRvL.110b8701G10.1103/PhysRevLett.110.028701 BattistonFNicosiaVLatoraVStructural measures for multiplex networksPhys. Rev. E2014890328042014PhRvE..89c2804B10.1103/PhysRevE.89.032804 SorrentinoFSynchronization of hypernetworks of coupled dynamical systemsNew J. Phys.2012140330352012NJPh...14c3035S10.1088/1367-2630/14/3/033035 De DomenicoMSolé-RibaltaAGómezSArenasANavigability of interconnected networks under random failuresProc. Natl Acad. Sci. USA2014111835183562014PNAS..111.8351D32628031355.9001410.1073/pnas.1318469111 MenichettiGRemondiniDPanzarasaPMondragónR JBianconiGWeighted multiplex networksPLoS ONE20149e978572014PLoSO...997857M10.1371/journal.pone.0097857 WangZWangLSzolnokiAPercMEvolutionary games on multilayer networks: a colloquiumEur. Phys. J. B2015881242015EPJB...88..124W10.1140/epjb/e2015-60270-7 Ferraz de Arruda, G., Cozzo, E., Peixoto, P. T., Rodrigues, F. A. & Moreno, Y. Epidemic spreading in interconnected networks: a continuous time approach. Preprint at http://arXiv.org/abs/1509.07054 (2015). DickisonMHavlinSStanleyH EEpidemics on interconnected networksPhys. Rev. E2012850661092012PhRvE..85f6109D10.1103/PhysRevE.85.066109 BazziMCommunity detection in temporal multilayer networks, with an application to correlation networksMultisc. Model. Simul.20161414134397531328.9015110.1137/15M1009615 BullmoreESpornsOThe economy of brain network organizationNat. Rev. Neurosci.20121333634910.1038/nrn3214 MuchaP JRichardsonTMaconKPorterM AOnnelaJ-PCommunity structure in time-dependent, multiscale, and multiplex networksScience20103288768782010Sci...328..876M26625901226.9105610.1126/science.1184819 ReisS DAvoiding catastrophic failure in correlated networks of networksNat. Phys.20141076276710.1038/nphys3081 NewmanME JNetworks: An Introduction20101195.9400310.1093/acprof:oso/9780199206650.001.0001 SpornsOBetzelR FModular brain networksAnnu. Rev. Psychol.20161519.119.28 BianconiGDorogovtsevS NMultiple percolation transitions in a configuration model of a network of networksPhys. Rev. E2014890628142014PhRvE..89f2814B10.1103/PhysRevE.89.062814 CardilloAEmergence of network features from multiplexitySci. Rep.20133134410.1038/srep01344 SanzJXiaC-YMeloniSMorenoYDynamics of interacting diseasesPhys. Rev. X20144041005 KiveläMMultilayer networksJ. Comp. Netw.2014220327110.1093/comnet/cnu016 HaluAMondragonR JPanzarasaPBianconiGMultiplex pagerankPLoS ONE20138e782932013PLoSO...878293H10.1371/journal.pone.0078293 WuZMenichettiGRahmedeCBianconiGEmergent complex network geometrySci. Rep.20155100732015NatSR...510073W10.1038/srep10073 Sevilla-EscobozaREnhancing the stability of the synchronization of multivariable coupled oscillatorsPhys. Rev. E2015920328042015PhRvE..92c2804S355319310.1103/PhysRevE.92.032804 EcheniquePGómez-GardeñesJMorenoYDynamics of jamming transitions in complex networksEurophys. Lett.2005713252005EL.....71..325E10.1209/epl/i2005-10080-8 FunkSNine challenges in incorporating the dynamics of behaviour in infectious diseases modelsEpidemics201510212510.1016/j.epidem.2014.09.005 ChungFR KSpectral Graph Theory19970867.05046 GuimeràRDíaz-GuileraAVega-RedondoFCabralesAArenasAOptimal network topologies for local search with congestionPhys. Rev. Lett.2002892487012002PhRvL..89x8701G10.1103/PhysRevLett.89.248701 GaoJBuldyrevS VStanleyH EHavlinSNetworks formed from interdependent networksNat. Phys.20128404810.1038/nphys2180 RadicchiFArenasAAbrupt transition in the structural formation of interconnected networksNat. Phys.2013971772010.1038/nphys2761 Gómez-GardenesJReinaresIArenasAFloríaL MEvolution of cooperation in multiplex networksSci. Rep.201226202012NatSR...2E.620G10.1038/srep00620 Taylor, D., Myers, S. A., Clauset, A., Porter, M. A. & Mucha, P. J. Eigenvector-based centrality measures for temporal networks. Preprint at http://arXiv.org/abs/1507.01266 (2015). FunkSGiladEWatkinsCJansenVA AThe spread of awareness and its impact on epidemic outbreaksProc. Natl Acad. Sci. USA2009106687268772009PNAS..106.6872F1203.9124210.1073/pnas.0810762106 AsllaniMBusielloD MCarlettiTFanelliDPlanchonGTuring patterns in multiplex networksPhys. Rev. E2014900428142014PhRvE..90d2814A10.1103/PhysRevE.90.042814 De DomenicoMSolé-RibaltaAOmodeiEGómezSArenasARanking in interconnected multilayer networks reveals versatile nodesNat. Commun.2015668682015NatCo...6.6868D10.1038/ncomms7868 PeixotoT PInferring the mesoscale structure of layered, edge-valued, and time-varying networksPhys. Rev. E2015920428072015PhRvE..92d2807P10.1103/PhysRevE.92.042807 KoldaT GBaderB WTensor decompositions and applicationsSIAM Rev.2009514555002009SIAMR..51..455K25350561173.6502910.1137/07070111X Papadopoulos, L., Puckett, J., Daniels, K. E. & Bassett, D. S. Evolution of network architecture in a granular material under compression. Preprint at http://arXiv.org/abs/1603.08159 (2016). GauvinLPanissonACattutoCDetecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approachPLoS ONE20149e860282014PLoSO...986028G10.1371/journal.pone.0086028 de Sola PoolIKochenMContacts and influenceSoc. Netw.1978155150660210.1016/0378-8733(78)90011-4 Pilosof, S., Porter, M. A. & Kéfi, S. Ecological multilayer networks: a new frontier for network ecology. Preprint at http://arXiv.org/abs/1511.04453 (2015). ZhangXBoccalettiSGuanSLiuZExplosive synchronization in adaptive and multilayer networksPhys. Rev. Lett.20151140387012015PhRvL.114c8701Z10.1103/PhysRevLett.114.038701 GleichD FPageRank beyond the WebSIAM Rev.20155732136333767601336.0512210.1137/140976649 LimaADe DomenicoMPejovicVMusolesiMDisease containment strategies based on mobility and information disseminationSci. Rep.20155106502015NatSR...510650L10.1038/srep10650 NicosiaVLatoraVMeasuring and modeling correlations in multiplex networksPhys. Rev. E2015920328052015PhRvE..92c2805N10.1103/PhysRevE.92.032805 BaxterG JDo L Zhao (BFnphys3865_CR59) 2005; 71 N Kouvaris (BFnphys3865_CR79) 2015; 5 BFnphys3865_CR7 S Funk (BFnphys3865_CR29) 2015; 10 B Min (BFnphys3865_CR43) 2014; 89 M A Porter (BFnphys3865_CR73) 2016 A Hackett (BFnphys3865_CR15) 2016; 6 BFnphys3865_CR69 J Gómez-Gardenes (BFnphys3865_CR33) 2012; 2 R Gallotti (BFnphys3865_CR37) 2016; 2 D Brockmann (BFnphys3865_CR81) 2013; 342 S Boccaletti (BFnphys3865_CR5) 2014; 544 F Tan (BFnphys3865_CR61) 2014; 89 BFnphys3865_CR64 D Krioukov (BFnphys3865_CR80) 2010; 82 S-W Son (BFnphys3865_CR12) 2012; 97 X Zhang (BFnphys3865_CR76) 2015; 114 Z Wang (BFnphys3865_CR36) 2015; 88 S D Reis (BFnphys3865_CR44) 2014; 10 V Nicosia (BFnphys3865_CR45) 2015; 92 G Menichetti (BFnphys3865_CR23) 2014; 9 M Asllani (BFnphys3865_CR78) 2014; 90 Z Wu (BFnphys3865_CR82) 2015; 5 S Gómez (BFnphys3865_CR50) 2013; 110 S V Buldyrev (BFnphys3865_CR9) 2010; 464 C Granell (BFnphys3865_CR30) 2013; 111 M De Domenico (BFnphys3865_CR38) 2015; 6 S Funk (BFnphys3865_CR65) 2009; 106 F Sorrentino (BFnphys3865_CR74) 2012; 14 F Battiston (BFnphys3865_CR19) 2014; 89 P J Mucha (BFnphys3865_CR39) 2010; 328 T G Kolda (BFnphys3865_CR53) 2009; 51 G Bianconi (BFnphys3865_CR22) 2013; 87 J Gao (BFnphys3865_CR10) 2012; 8 L Sola (BFnphys3865_CR17) 2013; 3 R G Morris (BFnphys3865_CR26) 2012; 109 M De Domenico (BFnphys3865_CR20) 2015; 6 M Bazzi (BFnphys3865_CR54) 2016; 14 M Salehi (BFnphys3865_CR35) 2015; 2 L Bargigli (BFnphys3865_CR71) 2015; 15 O Sporns (BFnphys3865_CR67) 2016; 15 G J Baxter (BFnphys3865_CR11) 2012; 109 BFnphys3865_CR55 BFnphys3865_CR56 I Abraham (BFnphys3865_CR84) 2015; 44 J Gómez-Gardeñes (BFnphys3865_CR47) 2015; 373 P Echenique (BFnphys3865_CR60) 2005; 71 M Barthelemy (BFnphys3865_CR83) 2011; 499 S Wasserman (BFnphys3865_CR3) 1994 G Bianconi (BFnphys3865_CR13) 2014; 89 E Cozzo (BFnphys3865_CR63) 2013; 88 R Guimerà (BFnphys3865_CR58) 2002; 89 L Gauvin (BFnphys3865_CR40) 2014; 9 R Gallotti (BFnphys3865_CR6) 2014; 4 R Sevilla-Escoboza (BFnphys3865_CR77) 2015; 92 U Braun (BFnphys3865_CR25) 2015; 112 F Radicchi (BFnphys3865_CR49) 2014; 4 ME J Newman (BFnphys3865_CR1) 2010 A Lima (BFnphys3865_CR32) 2015; 5 A Sole-Ribalta (BFnphys3865_CR51) 2013; 88 V Nicosia (BFnphys3865_CR70) 2015; 92 A Halu (BFnphys3865_CR18) 2013; 8 M De Domenico (BFnphys3865_CR16) 2013; 3 I de Sola Pool (BFnphys3865_CR72) 1978; 1 C Granell (BFnphys3865_CR66) 2014; 90 M Dickison (BFnphys3865_CR62) 2012; 85 A Cardillo (BFnphys3865_CR24) 2013; 3 Y Tang (BFnphys3865_CR75) 2014; 38 E Cozzo (BFnphys3865_CR21) 2015; 17 S Boccaletti (BFnphys3865_CR2) 2006; 424 D F Gleich (BFnphys3865_CR57) 2015; 57 A Solé-Ribalta (BFnphys3865_CR27) 2016; 116 M De Domenico (BFnphys3865_CR68) 2016; 10 K-M Lee (BFnphys3865_CR34) 2015; 88 F Radicchi (BFnphys3865_CR48) 2013; 9 M Kivelä (BFnphys3865_CR4) 2014; 2 FR K Chung (BFnphys3865_CR52) 1997 J Sanz (BFnphys3865_CR31) 2014; 4 B Min (BFnphys3865_CR14) 2014; 89 Z Wang (BFnphys3865_CR28) 2015; 15 T P Peixoto (BFnphys3865_CR42) 2015; 92 E Bullmore (BFnphys3865_CR8) 2012; 13 M De Domenico (BFnphys3865_CR41) 2015; 5 M De Domenico (BFnphys3865_CR46) 2014; 111 |
| References_xml | – reference: KouvarisNHataSDiaz-GuileraAPattern formation in multiplex networksSci. Rep.20155108402015NatSR...510840K10.1038/srep10840 – reference: BoccalettiSThe structure and dynamics of multilayer networksPhys. Rep.201454411222014PhR...544....1B327014010.1016/j.physrep.2014.07.001 – reference: MenichettiGRemondiniDPanzarasaPMondragónR JBianconiGWeighted multiplex networksPLoS ONE20149e978572014PLoSO...997857M10.1371/journal.pone.0097857 – reference: BoccalettiSLatoraVMorenoYChavezMHwangD-UComplex networks: structure and dynamicsPhys. Rep.20064241753082006PhR...424..175B21936211371.8200210.1016/j.physrep.2005.10.009 – reference: TanFWuJXiaYChiK TTraffic congestion in interconnected complex networksPhys. Rev. E2014890628132014PhRvE..89f2813T10.1103/PhysRevE.89.062813 – reference: FunkSGiladEWatkinsCJansenVA AThe spread of awareness and its impact on epidemic outbreaksProc. Natl Acad. Sci. USA2009106687268772009PNAS..106.6872F1203.9124210.1073/pnas.0810762106 – reference: GranellCGómezSArenasADynamical interplay between awareness and epidemic spreading in multiplex networksPhys. Rev. Lett.20131111287012013PhRvL.111l8701G10.1103/PhysRevLett.111.128701 – reference: ZhangXBoccalettiSGuanSLiuZExplosive synchronization in adaptive and multilayer networksPhys. Rev. Lett.20151140387012015PhRvL.114c8701Z10.1103/PhysRevLett.114.038701 – reference: SpornsOBetzelR FModular brain networksAnnu. Rev. Psychol.20161519.119.28 – reference: PeixotoT PInferring the mesoscale structure of layered, edge-valued, and time-varying networksPhys. Rev. E2015920428072015PhRvE..92d2807P10.1103/PhysRevE.92.042807 – reference: AsllaniMBusielloD MCarlettiTFanelliDPlanchonGTuring patterns in multiplex networksPhys. Rev. E2014900428142014PhRvE..90d2814A10.1103/PhysRevE.90.042814 – reference: Ferraz de Arruda, G., Cozzo, E., Peixoto, P. T., Rodrigues, F. A. & Moreno, Y. Epidemic spreading in interconnected networks: a continuous time approach. Preprint at http://arXiv.org/abs/1509.07054 (2015). – reference: MuchaP JRichardsonTMaconKPorterM AOnnelaJ-PCommunity structure in time-dependent, multiscale, and multiplex networksScience20103288768782010Sci...328..876M26625901226.9105610.1126/science.1184819 – reference: CardilloAEmergence of network features from multiplexitySci. Rep.20133134410.1038/srep01344 – reference: Sole-RibaltaASpectral properties of the Laplacian of multiplex networksPhys. Rev. E2013880328072013PhRvE..88c2807S10.1103/PhysRevE.88.032807 – reference: BattistonFNicosiaVLatoraVStructural measures for multiplex networksPhys. Rev. E2014890328042014PhRvE..89c2804B10.1103/PhysRevE.89.032804 – reference: Gómez-GardeñesJde DomenicoMGutiérrezGArenasAGómezSLayer–layer competition in multiplex complex networksPhil. Trans. R. Soc. A2015373201501172015RSPTA.37350117G10.1098/rsta.2015.0117 – reference: GallottiRPorterM ABarthelemyMLost in transportation: information measures and cognitive limits in multilayer navigationSci. Adv.20162e15004452016SciA....2E0445G10.1126/sciadv.1500445 – reference: De DomenicoMSolé-RibaltaAGómezSArenasANavigability of interconnected networks under random failuresProc. Natl Acad. Sci. USA2014111835183562014PNAS..111.8351D32628031355.9001410.1073/pnas.1318469111 – reference: MorrisR GBarthelemyMTransport on coupled spatial networksPhys. Rev. Lett.20121091287032012PhRvL.109l8703M10.1103/PhysRevLett.109.128703 – reference: CozzoEStructure of triadic relations in multiplex networksNew J. Phys.2015170730292015NJPh...17g3029C10.1088/1367-2630/17/7/073029 – reference: KrioukovDPapadopoulosFKitsakMVahdatABoguñáMHyperbolic geometry of complex networksPhys. Rev. E2010820361062010PhRvE..82c6106K278799810.1103/PhysRevE.82.036106 – reference: BuldyrevS VParshaniRPaulGStanleyH EHavlinSCatastrophic cascade of failures in interdependent networksNature2010464102510282010Natur.464.1025B10.1038/nature08932 – reference: SanzJXiaC-YMeloniSMorenoYDynamics of interacting diseasesPhys. Rev. X20144041005 – reference: BazziMCommunity detection in temporal multilayer networks, with an application to correlation networksMultisc. Model. Simul.20161414134397531328.9015110.1137/15M1009615 – reference: HaluAMondragonR JPanzarasaPBianconiGMultiplex pagerankPLoS ONE20138e782932013PLoSO...878293H10.1371/journal.pone.0078293 – reference: KoldaT GBaderB WTensor decompositions and applicationsSIAM Rev.2009514555002009SIAMR..51..455K25350561173.6502910.1137/07070111X – reference: Aldous, D. & Fill, J. A. Reversible Markov Chains and Random Walks on Graphs Unfinished monograph, recompiled 2014 (2002); https://www.stat.berkeley.edu/∼aldous/RWG/book.html – reference: CozzoEBanosR AMeloniSMorenoYContact-based social contagion in multiplex networksPhys. Rev. E2013880508012013PhRvE..88e0801C10.1103/PhysRevE.88.050801 – reference: Papadopoulos, L., Puckett, J., Daniels, K. E. & Bassett, D. S. Evolution of network architecture in a granular material under compression. Preprint at http://arXiv.org/abs/1603.08159 (2016). – reference: Sevilla-EscobozaREnhancing the stability of the synchronization of multivariable coupled oscillatorsPhys. Rev. E2015920328042015PhRvE..92c2804S355319310.1103/PhysRevE.92.032804 – reference: GómezSDiffusion dynamics on multiplex networksPhys. Rev. Lett.20131100287012013PhRvL.110b8701G10.1103/PhysRevLett.110.028701 – reference: DickisonMHavlinSStanleyH EEpidemics on interconnected networksPhys. Rev. E2012850661092012PhRvE..85f6109D10.1103/PhysRevE.85.066109 – reference: BianconiGStatistical mechanics of multiplex networks: entropy and overlapPhys. Rev. E2013870628062013PhRvE..87f2806B10.1103/PhysRevE.87.062806 – reference: NewmanME JNetworks: An Introduction20101195.9400310.1093/acprof:oso/9780199206650.001.0001 – reference: HackettACellaiDGómezSArenasAGleesonJ PBond percolation on multiplex networksPhys. Rev. X20166021002 – reference: ChungFR KSpectral Graph Theory19970867.05046 – reference: de Sola PoolIKochenMContacts and influenceSoc. Netw.1978155150660210.1016/0378-8733(78)90011-4 – reference: De DomenicoMSasaiSArenasAMapping multiplex hubs in human functional brain networkFront. Neurosci.20161000326 – reference: BaxterG JDorogovtsevS NGoltsevA VMendesJF FAvalanche collapse of interdependent networksPhys. Rev. Lett.20121092487012012PhRvL.109x8701B10.1103/PhysRevLett.109.248701 – reference: BianconiGDorogovtsevS NMultiple percolation transitions in a configuration model of a network of networksPhys. Rev. E2014890628142014PhRvE..89f2814B10.1103/PhysRevE.89.062814 – reference: ZhaoLLaiY-CParkKYeNOnset of traffic congestion in complex networksPhys. Rev. E2005710261252005PhRvE..71b6125Z10.1103/PhysRevE.71.026125 – reference: LeeK-MMinBGohK-ITowards real-world complexity: an introduction to multiplex networksEur. Phys. J. B201588482015EPJB...88...48L10.1140/epjb/e2015-50742-1 – reference: SalehiMSpreading processes in multilayer networksIEEE Trans. Netw. Sci. Eng.20152658310.1109/TNSE.2015.2425961 – reference: De DomenicoMNicosiaVArenasALatoraVStructural reducibility of multilayer networksNat. Commun.2015668642015NatCo...6.6864D10.1038/ncomms7864 – reference: WangZWangLSzolnokiAPercMEvolutionary games on multilayer networks: a colloquiumEur. Phys. J. B2015881242015EPJB...88..124W10.1140/epjb/e2015-60270-7 – reference: Solé-RibaltaAGómezSArenasACongestion induced by the structure of multiplex networksPhys. Rev. Lett.20161161087012016PhRvL.116j8701S10.1103/PhysRevLett.116.108701 – reference: BraunUDynamic reconfiguration of frontal brain networks during executive cognition in humansProc. Natl Acad. Sci. USA201511211678116832015PNAS..11211678B10.1073/pnas.1422487112 – reference: RadicchiFArenasAAbrupt transition in the structural formation of interconnected networksNat. Phys.2013971772010.1038/nphys2761 – reference: WangZAndrewsM AWuZ-XWangLBauchC TCoupled disease–behavior dynamics on complex networks: a reviewPhys. Life Rev.2015151292015PhLRv..15....1W10.1016/j.plrev.2015.07.006 – reference: MinBYiS DLeeK-MGohK-INetwork robustness of multiplex networks with interlayer degree correlationsPhys. Rev. E2014890428112014PhRvE..89d2811M10.1103/PhysRevE.89.042811 – reference: Pilosof, S., Porter, M. A. & Kéfi, S. Ecological multilayer networks: a new frontier for network ecology. Preprint at http://arXiv.org/abs/1511.04453 (2015). – reference: Gómez-GardenesJReinaresIArenasAFloríaL MEvolution of cooperation in multiplex networksSci. Rep.201226202012NatSR...2E.620G10.1038/srep00620 – reference: MinBDo YiSLeeK-MGohK-INetwork robustness of multiplex networks with interlayer degree correlationsPhys. Rev. E2014890428112014PhRvE..89d2811M10.1103/PhysRevE.89.042811 – reference: GauvinLPanissonACattutoCDetecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approachPLoS ONE20149e860282014PLoSO...986028G10.1371/journal.pone.0086028 – reference: AbrahamIChechikSKempeDSlivkinsALow-distortion inference of latent similarities from a multiplex social networkSIAM J. Comput.20154461766833526201422.9160410.1137/130949191 – reference: GaoJBuldyrevS VStanleyH EHavlinSNetworks formed from interdependent networksNat. Phys.20128404810.1038/nphys2180 – reference: FunkSNine challenges in incorporating the dynamics of behaviour in infectious diseases modelsEpidemics201510212510.1016/j.epidem.2014.09.005 – reference: GranellCGómezSArenasACompeting spreading processes on multiplex networks: awareness and epidemicsPhys. Rev. E2014900128082014PhRvE..90a2808G10.1103/PhysRevE.90.012808 – reference: PorterM AGleesonJ PDynamical Systems on Networks: A Tutorial20161369.3400110.1007/978-3-319-26641-1 – reference: ReisS DAvoiding catastrophic failure in correlated networks of networksNat. Phys.20141076276710.1038/nphys3081 – reference: GleichD FPageRank beyond the WebSIAM Rev.20155732136333767601336.0512210.1137/140976649 – reference: EcheniquePGómez-GardeñesJMorenoYDynamics of jamming transitions in complex networksEurophys. Lett.2005713252005EL.....71..325E10.1209/epl/i2005-10080-8 – reference: WuZMenichettiGRahmedeCBianconiGEmergent complex network geometrySci. Rep.20155100732015NatSR...510073W10.1038/srep10073 – reference: RadicchiFDriving interconnected networks to supercriticalityPhys. Rev. X20144021014 – reference: WassermanSFaustKSocial Network Analysis: Methods and Applications19940926.9106610.1017/CBO9780511815478 – reference: De DomenicoMSolé-RibaltaAOmodeiEGómezSArenasARanking in interconnected multilayer networks reveals versatile nodesNat. Commun.2015668682015NatCo...6.6868D10.1038/ncomms7868 – reference: BrockmannDHelbingDThe hidden geometry of complex, network-driven contagion phenomenaScience2013342133713422013Sci...342.1337B10.1126/science.1245200 – reference: NicosiaVLatoraVMeasuring and modeling correlations in multiplex networksPhys. Rev. E2015920328052015PhRvE..92c2805N10.1103/PhysRevE.92.032805 – reference: TangYQianFGaoHKurthsJSynchronization in complex networks and its application—a survey of recent advances and challengesAnnu. Rev. Control20143818419810.1016/j.arcontrol.2014.09.003 – reference: BullmoreESpornsOThe economy of brain network organizationNat. Rev. Neurosci.20121333634910.1038/nrn3214 – reference: KiveläMMultilayer networksJ. Comp. Netw.2014220327110.1093/comnet/cnu016 – reference: LimaADe DomenicoMPejovicVMusolesiMDisease containment strategies based on mobility and information disseminationSci. Rep.20155106502015NatSR...510650L10.1038/srep10650 – reference: SolaLEigenvector centrality of nodes in multiplex networksChaos201330331312013Chaos..23c3131S1323.0511710.1063/1.4818544 – reference: BargigliLDi IasioGInfanteLLilloFPierobonFThe multiplex structure of interbank networksQuant. Financ.20151567369133210851398.9170310.1080/14697688.2014.968356 – reference: GuimeràRDíaz-GuileraAVega-RedondoFCabralesAArenasAOptimal network topologies for local search with congestionPhys. Rev. Lett.2002892487012002PhRvL..89x8701G10.1103/PhysRevLett.89.248701 – reference: GallottiRBarthelemyMAnatomy and efficiency of urban multimodal mobilitySci. Rep.2014469112014NatSR...4E6911G10.1038/srep06911 – reference: SorrentinoFSynchronization of hypernetworks of coupled dynamical systemsNew J. Phys.2012140330352012NJPh...14c3035S10.1088/1367-2630/14/3/033035 – reference: BarthelemyMSpatial networksPhys. Rep.201149911012011PhR...499....1B277096210.1016/j.physrep.2010.11.002 – reference: SonS-WBizhaniGChristensenCGrassbergerPPaczuskiMPercolation theory on interdependent networks based on epidemic spreadingEurophys. Lett.201297160062012EL.....9716006S10.1209/0295-5075/97/16006 – reference: De DomenicoMMathematical formulation of multi-layer networksPhys. Rev. X20133041022 – reference: Taylor, D., Myers, S. A., Clauset, A., Porter, M. A. & Mucha, P. J. Eigenvector-based centrality measures for temporal networks. Preprint at http://arXiv.org/abs/1507.01266 (2015). – reference: De DomenicoMLancichinettiAArenasARosvallMIdentifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systemsPhys. Rev. X20155011027 – volume: 89 start-page: 032804 year: 2014 ident: BFnphys3865_CR19 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.032804 – volume: 5 start-page: 10650 year: 2015 ident: BFnphys3865_CR32 publication-title: Sci. Rep. doi: 10.1038/srep10650 – volume: 51 start-page: 455 year: 2009 ident: BFnphys3865_CR53 publication-title: SIAM Rev. doi: 10.1137/07070111X – volume: 10 start-page: 00326 year: 2016 ident: BFnphys3865_CR68 publication-title: Front. Neurosci. – volume: 9 start-page: 717 year: 2013 ident: BFnphys3865_CR48 publication-title: Nat. Phys. doi: 10.1038/nphys2761 – volume-title: Dynamical Systems on Networks: A Tutorial year: 2016 ident: BFnphys3865_CR73 doi: 10.1007/978-3-319-26641-1 – volume: 114 start-page: 038701 year: 2015 ident: BFnphys3865_CR76 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.114.038701 – volume: 464 start-page: 1025 year: 2010 ident: BFnphys3865_CR9 publication-title: Nature doi: 10.1038/nature08932 – volume: 9 start-page: e86028 year: 2014 ident: BFnphys3865_CR40 publication-title: PLoS ONE doi: 10.1371/journal.pone.0086028 – volume: 71 start-page: 026125 year: 2005 ident: BFnphys3865_CR59 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.71.026125 – volume: 4 start-page: 6911 year: 2014 ident: BFnphys3865_CR6 publication-title: Sci. Rep. doi: 10.1038/srep06911 – volume: 15 start-page: 1 year: 2015 ident: BFnphys3865_CR28 publication-title: Phys. Life Rev. doi: 10.1016/j.plrev.2015.07.006 – volume: 5 start-page: 011027 year: 2015 ident: BFnphys3865_CR41 publication-title: Phys. Rev. X – volume: 2 start-page: 620 year: 2012 ident: BFnphys3865_CR33 publication-title: Sci. Rep. doi: 10.1038/srep00620 – volume: 92 start-page: 032805 year: 2015 ident: BFnphys3865_CR45 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.032805 – volume: 8 start-page: e78293 year: 2013 ident: BFnphys3865_CR18 publication-title: PLoS ONE doi: 10.1371/journal.pone.0078293 – volume: 4 start-page: 041005 year: 2014 ident: BFnphys3865_CR31 publication-title: Phys. Rev. X – volume: 373 start-page: 20150117 year: 2015 ident: BFnphys3865_CR47 publication-title: Phil. Trans. R. Soc. A doi: 10.1098/rsta.2015.0117 – volume: 71 start-page: 325 year: 2005 ident: BFnphys3865_CR60 publication-title: Europhys. Lett. doi: 10.1209/epl/i2005-10080-8 – volume: 5 start-page: 10840 year: 2015 ident: BFnphys3865_CR79 publication-title: Sci. Rep. doi: 10.1038/srep10840 – volume: 15 start-page: 673 year: 2015 ident: BFnphys3865_CR71 publication-title: Quant. Financ. doi: 10.1080/14697688.2014.968356 – ident: BFnphys3865_CR64 – ident: BFnphys3865_CR69 doi: 10.1103/PhysRevE.94.032908 – volume: 10 start-page: 762 year: 2014 ident: BFnphys3865_CR44 publication-title: Nat. Phys. doi: 10.1038/nphys3081 – volume: 85 start-page: 066109 year: 2012 ident: BFnphys3865_CR62 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.85.066109 – volume: 57 start-page: 321 year: 2015 ident: BFnphys3865_CR57 publication-title: SIAM Rev. doi: 10.1137/140976649 – volume: 109 start-page: 128703 year: 2012 ident: BFnphys3865_CR26 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.128703 – volume: 13 start-page: 336 year: 2012 ident: BFnphys3865_CR8 publication-title: Nat. Rev. Neurosci. doi: 10.1038/nrn3214 – volume: 111 start-page: 8351 year: 2014 ident: BFnphys3865_CR46 publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.1318469111 – volume: 92 start-page: 032805 year: 2015 ident: BFnphys3865_CR70 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.032805 – volume: 2 start-page: 203 year: 2014 ident: BFnphys3865_CR4 publication-title: J. Comp. Netw. doi: 10.1093/comnet/cnu016 – volume: 3 start-page: 033131 year: 2013 ident: BFnphys3865_CR17 publication-title: Chaos doi: 10.1063/1.4818544 – volume: 110 start-page: 028701 year: 2013 ident: BFnphys3865_CR50 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.110.028701 – volume: 90 start-page: 012808 year: 2014 ident: BFnphys3865_CR66 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.90.012808 – volume: 14 start-page: 033035 year: 2012 ident: BFnphys3865_CR74 publication-title: New J. Phys. doi: 10.1088/1367-2630/14/3/033035 – volume: 87 start-page: 062806 year: 2013 ident: BFnphys3865_CR22 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.87.062806 – volume: 2 start-page: 65 year: 2015 ident: BFnphys3865_CR35 publication-title: IEEE Trans. Netw. Sci. Eng. doi: 10.1109/TNSE.2015.2425961 – ident: BFnphys3865_CR56 – volume: 9 start-page: e97857 year: 2014 ident: BFnphys3865_CR23 publication-title: PLoS ONE doi: 10.1371/journal.pone.0097857 – volume: 92 start-page: 042807 year: 2015 ident: BFnphys3865_CR42 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.042807 – volume: 89 start-page: 248701 year: 2002 ident: BFnphys3865_CR58 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.89.248701 – volume: 111 start-page: 128701 year: 2013 ident: BFnphys3865_CR30 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.111.128701 – volume: 10 start-page: 21 year: 2015 ident: BFnphys3865_CR29 publication-title: Epidemics doi: 10.1016/j.epidem.2014.09.005 – volume: 1 start-page: 5 year: 1978 ident: BFnphys3865_CR72 publication-title: Soc. Netw. doi: 10.1016/0378-8733(78)90011-4 – volume: 90 start-page: 042814 year: 2014 ident: BFnphys3865_CR78 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.90.042814 – volume: 499 start-page: 1 year: 2011 ident: BFnphys3865_CR83 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2010.11.002 – volume: 82 start-page: 036106 year: 2010 ident: BFnphys3865_CR80 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.82.036106 – volume: 97 start-page: 16006 year: 2012 ident: BFnphys3865_CR12 publication-title: Europhys. Lett. doi: 10.1209/0295-5075/97/16006 – volume: 116 start-page: 108701 year: 2016 ident: BFnphys3865_CR27 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.116.108701 – volume: 92 start-page: 032804 year: 2015 ident: BFnphys3865_CR77 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.92.032804 – volume-title: Networks: An Introduction year: 2010 ident: BFnphys3865_CR1 doi: 10.1093/acprof:oso/9780199206650.001.0001 – ident: BFnphys3865_CR7 – volume: 15 start-page: 19.1 year: 2016 ident: BFnphys3865_CR67 publication-title: Annu. Rev. Psychol. – volume-title: Social Network Analysis: Methods and Applications year: 1994 ident: BFnphys3865_CR3 doi: 10.1017/CBO9780511815478 – volume: 88 start-page: 050801 year: 2013 ident: BFnphys3865_CR63 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.88.050801 – volume-title: Spectral Graph Theory year: 1997 ident: BFnphys3865_CR52 – volume: 89 start-page: 042811 year: 2014 ident: BFnphys3865_CR43 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.042811 – volume: 38 start-page: 184 year: 2014 ident: BFnphys3865_CR75 publication-title: Annu. Rev. Control doi: 10.1016/j.arcontrol.2014.09.003 – volume: 328 start-page: 876 year: 2010 ident: BFnphys3865_CR39 publication-title: Science doi: 10.1126/science.1184819 – volume: 6 start-page: 021002 year: 2016 ident: BFnphys3865_CR15 publication-title: Phys. Rev. X – ident: BFnphys3865_CR55 – volume: 112 start-page: 11678 year: 2015 ident: BFnphys3865_CR25 publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.1422487112 – volume: 109 start-page: 248701 year: 2012 ident: BFnphys3865_CR11 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.109.248701 – volume: 544 start-page: 1 year: 2014 ident: BFnphys3865_CR5 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2014.07.001 – volume: 88 start-page: 48 year: 2015 ident: BFnphys3865_CR34 publication-title: Eur. Phys. J. B doi: 10.1140/epjb/e2015-50742-1 – volume: 6 start-page: 6864 year: 2015 ident: BFnphys3865_CR38 publication-title: Nat. Commun. doi: 10.1038/ncomms7864 – volume: 3 start-page: 041022 year: 2013 ident: BFnphys3865_CR16 publication-title: Phys. Rev. X – volume: 89 start-page: 062813 year: 2014 ident: BFnphys3865_CR61 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.062813 – volume: 88 start-page: 032807 year: 2013 ident: BFnphys3865_CR51 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.88.032807 – volume: 2 start-page: e1500445 year: 2016 ident: BFnphys3865_CR37 publication-title: Sci. Adv. doi: 10.1126/sciadv.1500445 – volume: 342 start-page: 1337 year: 2013 ident: BFnphys3865_CR81 publication-title: Science doi: 10.1126/science.1245200 – volume: 5 start-page: 10073 year: 2015 ident: BFnphys3865_CR82 publication-title: Sci. Rep. doi: 10.1038/srep10073 – volume: 17 start-page: 073029 year: 2015 ident: BFnphys3865_CR21 publication-title: New J. Phys. doi: 10.1088/1367-2630/17/7/073029 – volume: 3 start-page: 1344 year: 2013 ident: BFnphys3865_CR24 publication-title: Sci. Rep. doi: 10.1038/srep01344 – volume: 8 start-page: 40 year: 2012 ident: BFnphys3865_CR10 publication-title: Nat. Phys. doi: 10.1038/nphys2180 – volume: 89 start-page: 042811 year: 2014 ident: BFnphys3865_CR14 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.042811 – volume: 424 start-page: 175 year: 2006 ident: BFnphys3865_CR2 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2005.10.009 – volume: 88 start-page: 124 year: 2015 ident: BFnphys3865_CR36 publication-title: Eur. Phys. J. B doi: 10.1140/epjb/e2015-60270-7 – volume: 106 start-page: 6872 year: 2009 ident: BFnphys3865_CR65 publication-title: Proc. Natl Acad. Sci. USA doi: 10.1073/pnas.0810762106 – volume: 44 start-page: 617 year: 2015 ident: BFnphys3865_CR84 publication-title: SIAM J. Comput. doi: 10.1137/130949191 – volume: 89 start-page: 062814 year: 2014 ident: BFnphys3865_CR13 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.89.062814 – volume: 6 start-page: 6868 year: 2015 ident: BFnphys3865_CR20 publication-title: Nat. Commun. doi: 10.1038/ncomms7868 – volume: 4 start-page: 021014 year: 2014 ident: BFnphys3865_CR49 publication-title: Phys. Rev. X – volume: 14 start-page: 1 year: 2016 ident: BFnphys3865_CR54 publication-title: Multisc. Model. Simul. doi: 10.1137/15M1009615 |
| SSID | ssj0042613 |
| Score | 2.6630268 |
| SecondaryResourceType | review_article |
| Snippet | Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types... Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include dierent types... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 901 |
| SubjectTerms | 639/766/530/2801 639/766/530/2803 Analysis Atomic Classical and Continuum Physics Complex Systems Computer networks Condensed Matter Physics Couples Dynamical systems Mathematical and Computational Physics Mathematical models Molecular Multilayers Multiplexing Networks Optical and Plasma Physics Physics progress-article Spreading Theoretical |
| Title | The physics of spreading processes in multilayer networks |
| URI | https://link.springer.com/article/10.1038/nphys3865 https://www.proquest.com/docview/1825568368 https://www.proquest.com/docview/1845806042 |
| Volume | 12 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB60RfAiPrFaS3wcvCzdbpLN5iQqrUWwiFjobckThLKtbvv_TfbRahHPOyQwk535MvNlBuDGYkmkZDag1l1RiAqTIFEmCpSOY0MiInnxSOxlFA_H5HlCJ1XCLa9olbVPLBy1nimfI-86HOybZeE4uZt_Bn5qlK-uViM0tqHpXHDiLl_Nh_7o9a32xf5-gMsnkTSICMN1byGcdDOfOvATL39HpDXM3KiMFgFnsA97FVJE96VpD2DLZIewUzA2VX4E3BkYlXmJHM0scsuUfHg0L7n_JkcfGSoIg1PhgDXKSsZ3fgzjQf_9cRhUcxAChXlvEchQx0xpISNDQmOYplRjZngsmI2VjqxmnAnDnNsNJVWSMqMoFhjLMJKyx_AJNLJZZk4B9SQOleXcGCGJJVRyobkQzlAuUFkmW3Bb6yJVVZNwP6timhbFapykK7W14GolOi87Y_wl1K4VmlY_R56uTdmCy9Vnd6x9rUJkZrb0MoQmvrFP1ILr2hA_ltjc6Oz_jc5h1yGduGThtaGx-FqaC4cmFrID28ngqVMdnG_DEM5z |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LTxsxEB4BFYJL1fIQAQqmgMRllY0f6_WhqlBpGgrhBBK3xU8JKdoENhHqn-pvrL3OJoBQb5xt2dL4m_G8B-DIEUWV4i5hzpsoVKd5kmuLE22yzFJMlaiLxPpXWe-G_r5ltwvwt6mFCWmVjUysBbUZ6uAjb3s9ODTLIln-ffSQhKlRIbrajNCIsLiwf568yVZ9Oz_z73uMcffn9Y9eMp0qkGgiOuNEpSbj2kiFLU2t5YYxQ7gVmeQu0wY7wwWXlnshliqmFeNWMyIJUSlWqsOJP3cRPlBCROCovPurkfzBGiGxAJMlmHLSdDIiebsMjoowX_Pl_zdXal_FYevvrfsJPk71UnQagfQZFmy5Bst1fqiu1kF4OKHoBanQ0CF_TMy-R6NYaWArdF-iOj1xIL0aj8qYX15twM270GcTlsphabcAdRRJtRPCWqmoo0wJaYSUHhb-W3RcteCkoUWhpy3Jw2SMQVGHxklezMjWgq-zraPYh-OtTbsNQYspK1bFHDgtOJgteyYKkRFZ2uEk7KEsD22EcAsOm4d4dsTri7b_f9E-rPSu-5fF5fnVxQ6seh0ri_l_u7A0fpzYL16PGau9GjwI7t4brf8AyKoLcA |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1ZaxsxEB4ch4S-lCZNqNs0US_Iy-K1jtXqoZQcNjlaE0oCedvohIJZO1mH0r_WX1dpteschL7lWUKC0SfNjOabGYDPjiiqFHcJc95FoTrNk1xbnGiTZZZiqkSdJPZjnB1d0JNLdtmBv20uTKBVtm9i_VCbqQ5_5H1vB4diWSTL-66hRZwdjr7NrpPQQSpEWtt2GhEip_bPb---VV-PD_1Zf8F4NDw_OEqaDgOJJmIwT1RqMq6NVNjS1FpuGDOEW5FJ7jJtsDNccGm5f9BSxbRi3GpGJCEqxUoNOPHrLsEy915R2oXl_eH47GerB4JvQmI6Jksw5aSta0Tyfhm-LUK3zYfa8M7EfRSVrZXd6BW8bKxUtBdhtQYdW67DSs0W1dVrEB5cKP6JVGjqkF8mcvHRLOYd2Ar9KlFNVpxIb9SjMrLNqw24eBYJbUK3nJb2DaCBIql2QlgrFXWUKSGNkNKDxCtJx1UPdltZFLopUB76ZEyKOlBO8mIhth58XEydxaocT03aagVaNBezKu5g1IMPi2F_pUKcRJZ2ehvmUJaHokK4B5_ag7i3xOON3v5_ox1Y9Ugtvh-PT9_BC29wZZEMuAXd-c2tfe-NmrnabtCD4Oq5AfsPMKERAg |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+physics+of+spreading+processes+in+multilayer+networks&rft.jtitle=Nature+physics&rft.au=De+Domenico%2C+Manlio&rft.au=Granell%2C+Clara&rft.au=Porter%2C+Mason+A&rft.au=Arenas%2C+Alex&rft.date=2016-10-01&rft.issn=1745-2473&rft.volume=12&rft.issue=10&rft.spage=901&rft.epage=906&rft_id=info:doi/10.1038%2Fnphys3865&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1745-2473&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1745-2473&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1745-2473&client=summon |