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Neuroimaging data can be represented as networks of nodes and edges thatcapture the topological organization of the brain connectivity. Graph theoryprovides a general and powerful framework to study these networks and theirstructure at various scales. By way of example, community detection methodshave been widely applied to investigate the modular structure of many naturalnetworks, including brain functional connectivity networks. Sparsificationprocedures are often applied to remove the weakest edges, which are the mostaffected by experimental noise, and to reduce the density of the graph, thusmaking it theoretically and computationally more tractable. However, weak linksmay also contain significant structural information, and procedures to identifythe optimal tradeoff are the subject of active research. Here, we explore theuse of percolation analysis, a method grounded in statistical physics, toidentify the optimal sparsification threshold for community detection in brainconnectivity networks. By using synthetic networks endowed with a ground-truthmodular structure and realistic topological features typical of human brainfunctional connectivity networks, we show that percolation analysis can beapplied to identify the optimal sparsification threshold that maximizesinformation on the networks' community structure. We validate this approachusing three different community detection methods widely applied to theanalysis of brain connectivity networks: Newman's modularity, InfoMap andAsymptotical Surprise. Importantly, we test the effects of noise and datavariability, which are critical factors to determine the optimal threshold.This data-driven method should prove particularly useful in the analysis of thecommunity structure of brain networks in populations characterized by differentconnectivity strengths, such as patients and controls.

Graph analysis and modularity of brain functional connectivity networks: searching for the optimal threshold