Network Connectivity Models: An Overview and Applications

In recent years great attention has been paid to complex networks and to their related theories and models. In this context, the concepts of Small World and Scale Free Networks come to the fore. A Small World network (SW) is based on ‘six degrees of separation’, or the notion that everyone in the world is related to everyone else through at most six acquaintances. Small World Networks are similar in that they have a high degree of local clustering or cliquishness and a relatively short average minimum path, like a completely random network. A Scale Free (SF) network is principally characterized by an abundance of nodes with only a few links, while a very small number of nodes have a very large number of links, which are called hubs. This paper examines the above issues in the context of regional dynamics from both the methodological and empirical view point. In particular, the first part aims to provide an overview on the concepts, insights and research perspectives in spatial economics concerning SW and SF networks, in the light of their physical and statistical characteristics, e.g. diameter, clustering coefficient and vertex connectivity degree distribution. The second part of the paper attempts to explore some empirical applications in order to point out common features that characterize these networks in Socio and Spatial Economic Sector. The paper will end with methodological observations concerning the role of exponential/power law in the spatial economic literature.