Centrality Analysis of the United States Network Graph

Introduction

Network Science is one of the emerging fields of Data Science to analyze real-world networks from a graph theory point of view. Several real-world networks have been successfully modeled as undirected and directed graphs to study the intrinsic structural properties of the networks as well as the topological importance of nodes in these networks. The real-world networks that have been subjected to complex network analysis typically fall under one of these categories: social networks (Ghali et. al., 2012), transportation networks (Cheung & Gunes, 2012), biological networks (Ma & Gao, 2012), citation networks (Zhao & Strotmann, 2015), co-authorship networks (Ding, 2011) and etc. One category of real-world networks for which sufficient attention has not yet been given are the regional networks featuring the states within a country. In this chapter, we present a comprehensive analysis of a network graph of the states within a country with respect to the four commonly used centrality metrics in complex network analysis (Newman, 2010): degree, eigenvector, betweenness and closeness centralities.

We opine the chapter to serve as a model for anyone interested in analyzing a connected graph of the states within a country from a Network Science perspective. The approaches presented in this chapter could be useful to determine the states (and their cities) that are the most central and/or influential within a country. For example, the ranking of the vertices based on the shortest path centrality metrics (closeness and betweenness) could be useful to choose the states (and their cities) that could serve as hubs for transportation networks (like road and airline networks). We could identify the states that are most the central states as well as identify the states that could form a connected backbone and geographically well-connected to the rest of the states within a country and use this information to design the road/rail transportation networks. The degree centrality and eigenvector centrality metrics as well as the network-level metrics like minimum connected dominating set and maximal clique size could be useful to identify fewer number of venues (with several adjacent states to draw people) for political campaigns/meetings that would cover the entire country.