Clones in Social Networks

It is well known that any bipartite (social) network can be regarded as a formal context $(G,M,I)$. Therefore, such networks give raise to formal concept lattices which can be investigated utilizing the toolset of Formal Concept Analysis (FCA). In particular, the notion of clones in closure systems on $M$, i.e., pairwise interchangeable attributes that leave the closure system unchanged, suggests itself naturally as a candidate to be analyzed in the realm of FCA based social network analysis. In this study, we investigate the notion of clones in social networks. After building up some theoretical background for the clone relation in formal contexts we try to find clones in real word data sets. To this end, we provide an experimental evaluation on nine mostly well known social networks and provide some first insights on the impact of clones. We conclude our work by nourishing the understanding of clones by generalizing those to permutations of higher order.