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Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis

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  • Natarajan Meghanathan

Abstract

We seek to quantify the extent of similarity among nodes in a complex network with respect to two or more node-level metrics (like centrality metrics). In this pursuit, we propose the following unit disk graph-based approach: we first normalize the values for the node-level metrics (using the sum of the squares approach) and construct a unit disk graph of the network in a coordinate system based on the normalized values of the node-level metrics. There exists an edge between two vertices in the unit disk graph if the Euclidean distance between the two vertices in the normalized coordinate system is within a threshold value (ranging from 0 to , where k is the number of node-level metrics considered). We run a binary search algorithm to determine the minimum value for the threshold distance that would yield a connected unit disk graph of the vertices. We refer to “1 − (minimum threshold distance ) †as the node similarity index (NSI; ranging from 0 to 1) for the complex network with respect to the k node-level metrics considered. We evaluate the NSI values for a suite of 60 real-world networks with respect to both neighborhood-based centrality metrics (degree centrality and eigenvector centrality) and shortest path-based centrality metrics (betweenness centrality and closeness centrality).

Suggested Citation

  • Natarajan Meghanathan, 2019. "Unit Disk Graph-Based Node Similarity Index for Complex Network Analysis," Complexity, Hindawi, vol. 2019, pages 1-22, March.
  • Handle: RePEc:hin:complx:6871874
    DOI: 10.1155/2019/6871874
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