Theory of preference modelling for communities in scale-free networks

Abstract Detecting a community structure on networks is problem of interest in science and many other domains. Communities are special structures which may consist nodes with some common features. The identification overlapping communities can clarify not so apparent features about relationships among the network. A node have membership different degree. Here, we introduce fuzzy based approach for detection. type operator used to define strength community. Fuzzy systems logic branch mathematics introduces many-valued compute truth value. computed value between 0 1. preference modelling parameters designing particular strength. tells us what degree each member part As relevance applicability detection method types data various situations, this generates possibility user be able control overlap regions created while detecting communities. We extend existing methods use local function optimization LFM uses fitness identify structures. present pliant form provide mathematical proofs its properties, then apply implication continuous-valued logic. two important $$\nu$$ ν $$\alpha$$ α . parameter preference-implication allows design according our requirement defines sharpness implication. smaller threshold creates bigger more regions. higher stronger having participation controlled by $$\delta$$ δ relationship To balance creation regions, reducing outliers choose third such way that it controls varying as evolves over time. test theoretical model conducting experiments artificial real scale-free networks. behaviour all data-sets report found. In experiments, found good