Complex Network Analysis of the Contiguous United States Graph

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.

MINE: Identifying Top-k Vital Nodes in Complex Networks via Maximum Influential Neighbors Expansion

“…Meghanathan [86] proposes a normalization-based approach to obtain a comprehensive centrality ranking of the states in the graph of adjacencies from the map of USA. As concluded in his research, (i) the state of Missouri is the top-ranked node concerning all the commonly studied centrality measures, (ii) the state of Idaho has the lowest non-zero local clustering coefficient, indicating that the state is the most critical state with respect to facilitating communication between its neighboring states, (iii) the vital states measured by a single centrality is likely to be insufficient to exert strong influence on the whole network.…”