Revealing intricate properties of communities in the bipartite structure of online social networks

Many real-world networks based on human activities exhibit a bipartite structure. Although bipartite graphs seem appropriate to analyse and model their properties, it has been shown that standard metrics fail to reproduce intricate patterns observed in real networks. In particular, the overlapping of the neighbourhood of communities is difficult to capture precisely. In this work, we tackle this issue by analysing the structure of 4 real-world networks coming from online social activities. We first analyse their structure using standard metrics. Surprisingly, the clustering coefficient turns out to be less relevant than the redundancy coefficient to account for overlapping patterns. We then propose new metrics, namely the dispersion and the monopoly coefficients, and show that they help refining the study of bipartite overlaps. Finally, we compare the results obtained on real networks with the ones obtained on random bipartite models. This shows that the patterns captured by the redundancy and the dispersion coefficients are strongly related to the real nature of the observed overlaps.