6. Discussion and open problems

Throughout this article, we've seen how the problem of detecting communities in social networks began as a problem for sociologists, before becoming a problem for mathematicians and computer scientists. Following on from methods borrowed from data analysis, specific algorithms have recently appeared, some of which have become particularly efficient in terms of computation time and results, albeit to the detriment of providing less than optimal solutions. Various criteria for defining a good partition have been proposed, in particular modularity, whose probabilistic basis is scientifically founded. More recently, entropy and Nash equilibrium have provided additional scientific insights.

However, many questions remain unanswered. There remains, of course, the question of proposing new heuristics giving better results according to the various criteria already proposed...