In network science, assortativity refers to the tendency of links to exist between nodes with similar attributes. In social networks, for example, links tend to exist between individuals of similar age, nationality, location, race, income, educational level, religious belief, and language. Thus, various attributes jointly affect the network topology. An interesting problem is to detect community structure beyond some specific assortativity-related attributes $rho$, i.e., to take out the effect of $rho$ on network topology and reveal the hidden community structure which are due to other attributes. An approach to this problem is to redefine the null model of the modularity measure, so as to simulate the effect of $rho$ on network topology. However, a challenge is that we do not know to what extent the network topology is affected by $rho$ and by other attributes. In this paper, we propose Dist-Modularity which allows us to freely choose any suitable function to simulate the effect of $rho$. Such freedom can help us probe the effect of $rho$ and detect the hidden communities which are due to other attributes. We test the effectiveness of Dist-Modularity on synthetic benchmarks and two real-world networks.
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