Article,
Rich-Cores in Networks
PLOS ONE, 10 (3): e0119678+ (Mar 23, 2015)
DOI: 10.1371/journal.pone.0119678
Abstract
A core is said to be a group of central and densely connected nodes which
governs the overall behavior of a network. Profiling this meso--scale structure
currently relies on a limited number of methods which are often complex, and
have scalability issues when dealing with very large networks. As a result, we
are yet to fully understand its impact on network properties and dynamics. Here
we introduce a simple method to profile this structure by combining the
concepts of core/periphery and rich-club. The key challenge in addressing such
association of the two concepts is to establish a way to define the membership
of the core. The notion of a "rich-club" describes nodes which are essentially
the hub of a network, as they play a dominating role in structural and
functional properties. Interestingly, the definition of a rich-club naturally
emphasizes high degree nodes and divides a network into two subgroups. Our
approach theoretically couples the underlying principle of a rich-club with the
escape time of a random walker, and a rich-core is defined by examining changes
in the associated persistence probability. The method is fast and scalable to
large networks. In particular, we successfully show that the evolution of the
core in C. elegans and World Trade networks correspond to key
development stages and responses to historical events respectively.
