A fine-grained loop-level parallel approach to efficient fuzzy community detection in complex networks

Determining the inner organizational structure of sets of networked elements is of paramount importance to analyze real-world systems such as social, biological, or economic networks. To such an end, it is necessary to identify communities of interrelated nodes within the networks. Recently, a fuzzy community detection approach based on the minimization of a topological error functional has been proposed in the form of a gradient-based algorithm design pattern. However, the intrinsic quadratic algorithmic complexity of the procedure limits the problem size that can be efficiently treated. Here, we extend the ability of this approach to analyze larger networks resorting to parallelism. Thus, we identify the concurrency sources in the gradient-based algorithm design pattern. To determine the parallelization limits, we develop a two-dimensional performance model as a function of the number of processors and network size. The model permits to compute the maximum possible speedup. Another model is presented to find the maximum problem size tractable in a given amount of time. Application of the previous models to a set of benchmark networks shows that parallelization enhances the proposed fuzzy community detection approach in more than an order of magnitude. This allows treatment of networks with several hundred thousand nodes in a time frame of hours.