Estimating robustness in large social graphs

摘要

Given a large social graph, what can we say about its robustness? Broadly speaking, the property of robustness is crucial in real graphs, since it is related to the structural behavior of graphs to retain their connectivity properties after losing a portion of their edges/nodes. Can we estimate a robustness index for a graph quickly? Additionally, if the graph evolves over time, how this property changes? In this work, we are trying to answer the above questions studying the expansion properties of large social graphs. First, we present a measure that characterizes the robustness properties of a graph and also serves as global measure of the community structure (or lack thereof). We show how to compute this measure efficiently by exploiting the special spectral properties of real-world networks. We apply our method on several diverse real networks with millions of nodes, and we observe interesting properties for both static and time-evolving social graphs. As an application example, we show how to spot outliers and anomalies in graphs over time. Finally, we examine how graph generating models that mimic several properties of real-world graphs and behave in terms of robustness dynamics.