Dynamic community detection in a network of Kuramoto oscillators. (A

*, top*) The coupling matrix between

*N* = 128 phase oscillators contains 8 communities, each of which has 16 nodes. (A

*, bottom*) Over time, oscillators synchronize with one another. Color indicates the mean phase correlation between oscillators, where hotter (darker gray) colors indicate stronger correlations. (B) Phase correlation between oscillators as a function of time. The mean phase correlation between oscillators in the same community (dashed red curve) increases faster than the mean phase correlation between all oscillators in the system (solid gray curve). Regime I encompasses the first 50 time steps, and regime II emcompasses the subsequent 50 time steps. (C) Variance of maximized multilayer modularity (left), number of communities (middle), and partition similarity

*z* (right) over 100 optimizations of the multilayer modularity quality function for the temporal network in regime II as a function of the structural resolution parameter for

. The shaded gray area indicates values of the structural resolution parameter that provide 0 variance in the number of communities. (D) Example partition of the temporal network in regime II at

, which occurs near the troughs in panel (C). (E) Example partition of the temporal network in regime I at

. (F) Number of communities as a function of time for (

*left*) the temporal network in regime I and (

*right*) its corresponding temporal null model. We averaged values over

*C* = 100 optimizations of multilayer modularity.

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