| We know that communities in networks often overlap such that nodes simultaneously belong to several groups. Additionally, many networks are known to possess hierarchical organization, where communities are recursively grouped into a hierarchical structure. However, when each and every node belongs to more than one group, a single global hierarchy of nodes cannot capture the relationships between overlapping groups. Here we define communities as groups of links rather than nodes and show that this approach reconciles the ideas underlying overlapping communities and hierarchical organization. Further, we discuss the issue of percolation in graphs with pervasive overlap and implications for non-overlapping communities and network dynamics. Finally, the talk will address the general problem of proper validation of detected communities and suggest a solution, based on real networks with available metadata (which will be applied to assess the quality of the link-communities). |
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