On the utilization of shortest paths in complex networks

Abstract

Considerable effort has been devoted to the study of network structures and connectivity patterns and their influence on network dynamics. A widely used assumption in network analysis models is that traffic follows the shortest paths connecting pairs of nonneighboring vertices. For example, graph centrality measures, community extraction algorithms, and core-periphery detection algorithms use this assumption. However, this is a very restricted perspective and can be misleading as a consequence of its focus on shortest path communications. In this work, we study the utilization of shortest paths in complex networks in different data dissemination scenarios. We also explore whether there are general properties that can make networks utilize shortest paths more effectively. By conducting simulations on a set of real-world and artificial networks, we show that the utilization of shortest paths in complex networks may not be as common as assumed. This implies that longer paths can be as important (in some cases) as the shortest paths. Our results show that at least two factors clearly influence shortest path utilization in a network: the structure of the network and the data dissemination algorithm. We also find that the type of a network is not a good indicator of its shortest path utilization.