How a network breaks up into subnetworks or communities is of wide interest. Here we show that vertices connected to many other vertices across a network can disturb the community structures of otherwise ordered networks, introducing noise. We investigate strategies to identify and remove noisy vertices (“violators”) and develop a quantitative approach using statistical breakpoints to identify when the largest enhancement to a modularity measure is achieved. We show that removing nodes thus identified reduces noise in detected community structures for a range of different types of real networks in software systems and in biological systems.
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