Phase transition in spectral clustering based on resistance matrix

Abstract Community detection is a significant strategy to reveal the structure and function of real-world networks, especially in the era of social big data. Compared with the traditional spectral clustering algorithm for community detection, the spectral clustering algorithm based on resistance matrix reduces the computational complexity. In this work, we first show the presence of a phase transition for community detection strategy based on resistance matrix and show the critical condition in the accuracy of community detection. In detail, when the resistance distance r 3 between subnetworks C i ( i = 1 , 2 ) approaches r ∗ = n 1 r 1 + n 2 r 2 n , the detectability of community detection mutates suddenly, where r i ( i = 1 , 2 ) is the mean resistance distance of C i . Finally, the actual critical value is verified by simulation experiments.