A Geometric Preferential Attachment Model of Networks II

• Published in: Algorithms and Models for the Web-Graph pp. 41 - 55
• Main Authors: Flaxman, Abraham D., Frieze, Alan M., Vera, Juan
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Lecture Notes in Computer Science
• Subjects: Degree Distribution; Degree Sequence; Expansion Property; Preferential Attachment; Random Graph
• ISBN: 9783540770039; 3540770038
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-540-77004-6_4

A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp . We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law degree distribution where the expansion property depends on a tunable parameter of the model. The vertices of Gn are n sequentially generated points x1,x2,...,xn chosen uniformly at random from the unit sphere in . After generating xt, we randomly connect it to m points from those points in x1,x2,...,xt − 1 ...