Complex networks with scale-free nature and hierarchical modularity

TL;DR

This paper introduces the concept of mediating capacity in nodes, explaining how it leads to the emergence of scale-free and hierarchical modular structures in complex networks, and provides insights into their robustness and dynamics.

Contribution

It proposes mediating capacity as a key property influencing network structure, linking local node processes to global scale-free and hierarchical features.

Findings

Mediating capacity decreases with node degree, weakening hubs as mediators.

Explains the coexistence of scale-free structure and hierarchical modularity.

Provides insights into network robustness and control mechanisms.

Abstract

Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many networked systems like biological cell, human society and World Wide Web markedly deviate from that of completely random networks indicating the presence of underlying processes. Often the main process involved in their evolution is the addition of links between existing nodes having a common neighbor. In this context we introduce an important property of the nodes, which we call mediating capacity, that is generic to many networks. This capacity decreases rapidly with increase in degree, making hubs weak mediators of the process. We show that this property of nodes provides an explanation for the simultaneous occurrence of the observed scale-free structure and hierarchical modularity in many networked systems. This also explains the high clustering and small-path length seen in real networks as well as non-zero degree-correlations. Our study also provides insight into the local process which ultimately leads to emergence of preferential attachment and hence is also important in understanding robustness and control of real networks as well as processes happening on real networks.