Category: Network Sci.

Summary: Measuring how community structure changes consensus-time scaling in the voter model across a wide range of modularity levels.

The voter model reaches consensus quickly on well-mixed networks, but modular networks create a bottleneck between fast agreement inside communities and slow drift between them. This experiment asks how consensus time changes as inter-community connectivity becomes weaker relative to within-community connectivity.

The simulation sweeps the ratio of external to internal connection probability over several decades for multiple sizes and community counts. By doing so, it aims to map the full crossover from ordinary consensus scaling to a bottleneck-dominated regime where community structure strongly delays agreement.

That matters because many earlier studies inspect only a few modularity values. Here the emphasis is on the scaling function itself and on how finite-size effects shape the transition between mixing and modular trapping.

Method: Repeated voter-model simulations on stochastic block models, sweeping the ratio of inter-community to intra-community connectivity across sizes and community counts.

What is measured: Consensus time, crossover with modularity, dependence on community count, and finite-size scaling behavior.