Abstract
We model the contiguous states (48 states and the District of Columbia) of the United States (US) as an undirected network graph with each state represented as a node and there is an edge between two nodes if the corresponding two states share a common border. We determine a ranking of the states in the US with respect to a suite of node-level metrics: the centrality metrics (degree, eigenvector, betweenness and closeness), eccentricity, maximal clique size, and local clustering coefficient. We propose a normalization-based approach to obtain a comprehensive centrality ranking of the vertices (that is most likely to be tie-free) encompassing the normalized values of the four centrality metrics. We have applied the proposed normalization-based approach on the US States graph to obtain a tie-free ranking of the vertices based on a comprehensive centrality score. We observe the state of Missouri to be the most central state with respect to all the four centrality metrics. We have also analyzed the US States graph with respect to a suite of network-level metrics: bipartivity index, assortativity index, modularity, size of the minimum connected dominating set, algebraic connectivity and degree metrics. The approach taken in this paper could be useful for several application domains: transportation networks (to identify central hubs), politics (to identify campaign venues with larger geographic coverage), cultural and electoral studies (to identify communities of states that are relatively proximal to each other) and etc.
Highlights
Network Science is one of the emerging fields of Data Science to analyze real-world networks from a graph theory point of view
We present a comprehensive analysis of a network graph of the states within a country with respect to various node-level and network-level metrics typically considered in the field of Network Science and demonstrate the utility of information that can be obtained from the analysis
Our high-level contribution in this paper is to illustrate complex network analysis of a connected graph of the states within a country at node-level and network-level as well as propose a normalization-based approach to comprehensively rank the vertices in a network graph based on the centrality metrics
Summary
Network Science is one of the emerging fields of Data Science to analyze real-world networks from a graph theory point of view. We present a comprehensive analysis of a network graph of the states within a country with respect to various node-level and network-level metrics typically considered in the field of Network Science and demonstrate the utility of information that can be obtained from the analysis. 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
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