Clones in Graphs

TL;DR

This paper introduces a novel method for identifying structural similarities in graphs by using clique-preserving mappings and clone items, supported by theoretical insights and extensive experiments on real-world data.

Contribution

It proposes a new approach based on clone items and bipartite graph mappings, extending the concept to permutations, with comprehensive experimental validation.

Findings

Effective identification of graph similarities using clone-based methods

Extension of clone concepts to permutations

Empirical validation on real-world datasets

Abstract

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.