Detection of multiple and overlapping bidirectional communities within large, directed and weighted networks of neurons

With the recent explosion of publicly available biological data, the analysis of networks has gained significant interest. In particular, recent promising results in Neuroscience show that the way neurons and areas of the brain are connected to each other plays a fundamental role in cognitive functions and behaviour. Revealing pattern and structures within such an intricate volume of connections is a hard problem that has its roots in Graph and Network Theory. Since many real world situations can be modelled through networks, structures detection algorithms find application in almost every field of Science. These are NP-complete problems; therefore the generally used approach is through heuristic algorithms. Here, we formulate the problem of finding structures in networks of neurons in terms of a community detection problem. We introduce a definition of community and we construct a statistics-based heuristic algorithm for directed and weighted networks aiming at identifying overlapping bidirectional communities in large networks. We carry out a systematic analysis of the algorithm's performance, showing excellent results over a wide range of parameters (successful detection percentages almost $100\%$ all the time). Also, we show results on the computational time needed and we suggest future directions on how to improve computational performance.