Fig 1. Schematic representing the construction of a multilayer network for use in multi-scale modularity maximization.

Duplicates of a graph are connected in a multilayer fashion to construct a 3D graph. The smallest resolution parameter γ is assigned to the first layer (x), and it is linearly increased for the neighboring layers (y, z). The topological scale coupling parameter, τ, tunes the strength of the dependence of communities across layers. Since the community assignments are dependent on the adjacent layers, nodes that display high clustering over neighboring topological scales are identified as a single community spanning several scales. In this schematic, the large communities identified at initial layers progressively break into smaller sub-communities, revealing the hierarchical community organization of the graph.