Structure-dynamics interplay in directed complex networks with border effects

Abstract

Despite the large number of structural and dynamical properties investigated on complex networks, understanding their interrelationships is also of substantial importance to advance our knowledge on the organizing principles underlying such structures. We use a novel approach to study structure-dynamics correlations where the nodes of directed complex networks were partitioned into border and non-border by using the so-called diversity measurement. The network topology is characterized by the node degree, the most direct indicator of node connectivity, while the dynamics is related to the steady-state random walker occupation probability (called here node activity). Correlations between degree and activity were then analyzed inside and outside the border, separately. The obtained results showed that the intricate correlations found in the macaque cortex and in a WWW subgraph are in fact composed of two separate correlations of in-degree against the activity occurring inside and outside the border. These findings pave the way to investigations of possibly similar behavior in other directed complex networks. © 2011 Springer-Verlag.