Community Deception in Large Networks: Through the Lens of Laplacian Spectrum

• Published in: IEEE transactions on computational social systems Vol. 11; no. 2; pp. 1 - 13
• Main Authors: Zhang, Chong, Fu, Luoyi, Ding, Jiaxin, Cao, Xinde, Long, Fei, Wang, Xinbing, Zhou, Lei, Zhang, Jing, Zhou, Chenghu
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Community deception (CD); community detection; Detection algorithms; Eigenvalues; Eigenvalues and eigenfunctions; Image edge detection; Laplace equations; Laplacian spectrum; large network; Lenses; Perturbation methods; Social networking (online); Social networks
• ISSN: 2329-924X; 2373-7476
• DOI: 10.1109/TCSS.2023.3268564

Many complex networks in the real world have community structures. Typical examples include online social networks and ecology networks. While the identification of communities bears numerous practical applications, with the increasing awareness of data security and privacy concerns, the need to protect the community affiliations of individuals from disclosing by attackers emerges. This raises the community deception (CD) problem, that is, the opposite of community detection, which asks for ways to minimally perturb the network structures by rewiring nodes so that the target communities maximally hide themself from community detection algorithms. To this end, we investigate the CD problem through a Laplacian spectrum lens and propose a method named <inline-formula> <tex-math notation="LaTeX">\mathtt{ComDeceptor}</tex-math> </inline-formula> to hide a flexible target set of communities, which is more universal than most existing methods that either focus on hiding the entire communities or a single community. The key idea of <inline-formula> <tex-math notation="LaTeX">\mathtt{ComDeceptor}</tex-math> </inline-formula> is to first allocate the resources of perturbations fairly and effectively. By proving that hiding communities through intercommunity edge addition and intracommunity edge deletion correspond to maximizing the second smallest eigenvalue <inline-formula> <tex-math notation="LaTeX">\lambda_2</tex-math> </inline-formula> and minimizing the largest eigenvalue <inline-formula> <tex-math notation="LaTeX">\lambda_n</tex-math> </inline-formula> of the graph Laplacian, respectively, <inline-formula> <tex-math notation="LaTeX">\mathtt{ComDeceptor}</tex-math> </inline-formula> then incorporates efficient heuristics for approximately solving the problems, thus selecting the appropriate edge to perturb. Experimental results over nine real-world networks and six community detection algorithms not only demonstrate the efficiency of <inline-formula> <tex-math notation="LaTeX">\mathtt{ComDeceptor}</tex-math> </inline-formula>, but also the superior performance on obfuscating community structures over the baselines.