# Modeling and Measuring Graph Similarity: The Case for Centrality Distance

arXiv: https://arxiv.org/abs/1406.5481 · HTML: https://mlsanity.com/paper/1406.5481/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2014.

## Built on by (most cited first, 3 of 3)

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- [PURL: Safe and Effective Sanitization of Link Decoration](https://mlsanity.com/paper/2308.03417/) (2023)
- [On metric choice in dimension reduction for Fr'echet regression](https://mlsanity.com/paper/2410.01783/) (2024)

## Abstract (arXiv)

The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks. However, surprisingly little is known today about models to compare complex graphs, and quantitatively measure their similarity. This paper proposes a natural similarity measure for complex networks: centrality distance, the difference between two graphs with respect to a given node centrality. Centrality distances allow to take into account the specific roles of the different nodes in the network, and have many interesting applications. As a case study, we consider the closeness centrality in more detail, and show that closeness centrality distance can be used to effectively distinguish between randomly generated and actual evolutionary paths of two dynamic social networks.