We introduce a new conception of community structure, which we refer to as hidden community structure. Hidden community structure refers to a specific type of overlapping community structure, in which the detection of weak, but meaningful, communities is hindered by the presence of stronger communities. We present Hidden Community Detection HICODE, an algorithm template that identifies both the strong, dominant community structure as well as the weaker, hidden community structure in networks. HICODE begins by first applying an existing community detection algorithm to a network, and then removing the structure of the detected communities from the network. In this way, the structure of the weaker communities becomes visible. Through application of HICODE, we demonstrate that a wide variety of real networks from different domains contain many communities that, though meaningful, are not detected by any of the popular community detection algorithms that we consider. Additionally, on both real and synthetic networks containing a hidden ground-truth community structure, HICODE uncovers this structure better than any baseline algorithms that we compared against. For example, on a real network of undergraduate students that can be partitioned either by Dorm' (residence hall) or Year', we see that HICODE uncovers the weaker Year' communities with a JCRecall score (a recall-based metric that we define in the text) of over 0.7, while the baseline algorithms achieve scores below 0.2.
The Louvain method is a heuristic algorithm for modularity maximization that builds a hierarchy of communities by first optimizing modularity locally and then grouping small communities together into larger communities @cite_3 .
@cite_3
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We propose a simple method to extract the community structure of large networks. Our method is a heuristic method that is based on modularity optimization. It is shown to outperform all other known community detection methods in terms of computation time. Moreover, the quality of the communities detected is very good, as measured by the so-called modularity. This is shown first by identifying language communities in a Belgian mobile phone network of 2 million customers and by analysing a web graph of 118 million nodes and more than one billion links. The accuracy of our algorithm is also verified on ad hoc modular networks.