Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results.

Obtaining Communities with a Fitness Growth Process

The study of community structure has been a hot topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the ones by Lancichinetti et al. and Palla et al. arose as an answer to the resolution limit and degeneracies that modularity has. Here we start from the algorithm by Lancichinetti et al. and propose a unique growth process for a fitness function that, while being local, finds a community partition that covers the whole network, updating the scale parameter dynamically. We test the quality of our results by using a set of benchmarks of heterogeneous graphs. We discuss alternative measures for evaluating the community structure and, in the light of them, infer possible explanations for the better performance of local methods compared to global ones in these cases.