Graphlets over time: a new lens for analyzing growing networks

Abstract

Graphs are widely used for modeling various types of systems and information, including telephone communications, hyperlinks between web pages, and road networks. Many of such networks (i.e., graphs that model real-world systems and information) are growing, i.e., new nodes and edges appear over time. Counting the instances of each graphlet (i.e., an induced subgraph isomorphism class) has been successful in characterizing local structures of networks, with numerous applications. While graphlets have been extended for analysis of growing networks, the extensions are designed for examining temporally-local subgraphs composed of edges with close arrival time, instead of long-term changes in local structures. In this paper, as a new lens for growing network analysis, we study the evolution of distributions of graphlet instances over time in various networks at three different levels (graphs, nodes, and edges). At the graph level, we first discover that the evolution patterns are significantly different from those in random graphs. Then, we suggest a graphlet transition graph for measuring the similarity of the evolution patterns of graphs, and we find out a surprising similarity between the graphs from the same domain. At the node and edge levels, we demonstrate that the local structures around nodes and edges in their early stage provide a strong signal regarding their future importance. In particular, we significantly improve the predictability of the future importance of nodes and edges using the counts of the roles (a.k.a., orbits) that they take within graphlets.