Topology and Dynamics in Complex Networks: The Role of Edge Reciprocity

A key issue in complex systems regards the relationship between topology and dynamics. In this work, we use a recently introduced network property known as steering coefficient as a means to approach this issue with respect to different directed complex network systems under varying dynamics. Theoretical and real-world networks are considered, and the influences of reciprocity and average degree on the steering coefficient are quantified. A number of interesting results are reported that can assist the design of complex systems exhibiting larger or smaller relationships between topology and dynamics

Random walks in directed modular networks

Because diffusion typically involves symmetric interactions, scant attention has been focused on studying asymmetric cases. However, important networked systems underlain by diffusion (e.g. cortical networks and WWW) are inherently directed. In the case of undirected diffusion, it can be shown that the steady-state probability of the random walk dynamics is fully correlated with the degree, which no longer holds for directed networks. We investigate the relationship between such probability and the inward node degree, which we call efficiency, in modular networks. Our findings show that the efficiency of a given community depends mostly on the balance between its ingoing and outgoing connections. In addition, we derive analytical expressions to show that the internal degree of the nodes do not play a crucial role in their efficiency, when considering the Erd\H{o}s-R\'enyi and Barab\'asi-Albert models. The results are illustrated with respect to the macaque cortical network, providing subsidies for improving transportation and communication systems