Exploring the limits of community detection strategies in complex networks

The characterization of network community structure has profound implications in several scientific areas. Therefore, testing the algorithms developed to establish the optimal division of a network into communities is a fundamental problem in the field. We performed here a highly detailed evaluation of community detection algorithms, which has two main novelties: 1) using complex closed benchmarks, which provide precise ways to assess whether the solutions generated by the algorithms are optimal; and, 2) A novel type of analysis, based on hierarchically clustering the solutions suggested by multiple community detection algorithms, which allows to easily visualize how different are those solutions. Surprise, a global parameter that evaluates the quality of a partition, confirms the power of these analyses. We show that none of the community detection algorithms tested provide consistently optimal results in all networks and that Surprisemaximization, obtained by combiningmultiple algorithms, obtains quasi-optimal performances in these difficult benchmarks. C omplex networks are widely used for modeling real-world systems in very diverse areas, such as sociology, biology and physics1,2. It often occurs that nodes in these networks are arranged in tightly knit groups, which are called communities. Knowing the community structure of a network provides not only informa