Analysis of biologically inspired Small-World networks

Abstract

Small-World networks are highly clusterized networks with small distances between their nodes. There are some well known biological networks that present this kind of connectivity. On the other hand, the usual models of Small-World networks make use of undirected and unweighted graphs in order to represent the connectivity between the nodes of the network. These kind of graphs cannot model some essential characteristics of neural networks as, for example, the direction or the weight of the synaptic connections. In this paper we analyze different kinds of directed graphs and show that they can also present a Small-World topology when they are shifted from regular to random. Also analytical expressions are given for the cluster coefficient and the characteristic path of these graphs. © Springer-Verlag Berlin Heidelberg 2002.