Rich-cores in networks

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 \emph{C. elegans} and World Trade networks correspond to key development stages and responses to historical events respectively.

12 pages, 6 figures

References in corpus (9)

• Finding community structure in networks using the eigenvectors of matrices
• Cooperative Game Theory Approaches for Network Partitioning
• Reaction-diffusion processes and metapopulation models in heterogeneous networks
• New Model of Internet Topology Using k-shell Decomposition
• Structure and dynamics of core-periphery networks
• Core-periphery organization of complex networks
• On the rich-club effect in dense and weighted networks
• Rich-club vs rich-multipolarization phenomena in weighted networks
• VIP-club phenomenon: emergence of elites and masterminds in social networks

Cited by in corpus (18)

• Finding multiple core-periphery pairs in networks
• Community Detection in Large Hypergraphs
• Core-periphery structure requires something else in the network
• Multiplex core-periphery organization of the human connectome
• Resilience or Robustness: Identifying Topological Vulnerabilities in Rail Networks
• Reconstructing networks
• Disrupted core-periphery structure of multimodal brain networks in Alzheimer's Disease
• The impact of inter-city mobility on urban welfare
• Rich-Club Ordering and the Dyadic Effect: Two Interrelated Phenomena
• Generalized Rich-Club Ordering in Networks
• Random Spatial Network Models with Core-Periphery Structure
• Geometric explanation of the rich-club phenomenon in complex networks
• Impact of natural disasters on consumer behavior: case of the 2017 El Nino phenomenon in Peru
• The Atlas for the Aspiring Network Scientist
• The behavior of rich-club coefficient in scale-free networks
• Multiscale modeling of brain network organization
• Quantifying Networked Resilience via Multi-Scale Feedback Loops in Water Distribution Networks
• Core-biased random walks in complex networks