What is Eigenvector Centrality

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 the four commonly studied centrality metrics: degree, eigenvector, betweenness and closeness. We observe the states of Missouri and Maine to be respectively the most central state and the least central state with respect to all the four centrality metrics. The degree distribution is bi-modal Poisson. The eigenvector and closeness centralities also exhibit Poisson distribution, while the betweenness centrality exhibits power-law distribution. We observe a higher correlation in the ranking of vertices based on the degree centrality and betweenness centrality.