Centrality Analysis of a Weighted Iranian Provinces Adjacency Network

Document Type : Research Article

Author

Department of Computer Science, Khansar Campus, University of Isfahan, Isfahan, Iran.

Abstract

Recently, network theory has gained prominence for modeling and analyzing a wide range of phenomena to achieve a deeper understanding. In this paper, an undirected weighted network is employed to model the adjacency structure of the provinces of Iran. Each province is represented by a node in the network, and whenever two provinces share a boundary, a weighted edge is established between them. The edge weight is determined by the distance between the centers of the two adjacent provinces and lies in the interval [0,1]; closer provincial centers yield weights nearer to 1. The resulting network, hereafter termed the Weighted Iranian Provinces Adjacency Network (WIPAN), is analyzed to extract key network statistics. However, the core focus of the study involves the computation of various centrality measures on this network. For this analysis, twelve well-established centrality metrics-widely utilized in network science literature-were selected. This suite encompasses both fundamental measures, such as degree, closeness, and betweenness centrality, and more advanced or hybrid methods, including Katz, eigenvector, PageRank, and Laplacian centrality. Each method, viewed from its own standpoint, answers which nodes are most central in the network. Based on a consensus ranking of the centrality measures, node 10 emerges as the most central node in the network, while node 22 is the least central. The findings of this study establish a foundational basis for further analyses and can be applied to a broad range of planning problems as well as to decision-making at both micro and macro levels.

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References

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History

  • Receive Date: 22 October 2025
  • Revise Date: 21 June 2026
  • Accept Date: 23 June 2026

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