Detecting modules in dense weighted networks with the Potts method

TL;DR

This paper extends the q-state Potts method to detect modules in dense weighted networks, demonstrating its effectiveness on synthetic and real stock correlation data, with a focus on resolution tuning.

Contribution

It introduces a weighted version of the Potts method suitable for dense networks and analyzes its resolution dependence, applying it to financial data.

Findings

The weighted Potts method effectively detects modules in dense networks.

Resolution depends on tuning parameters and network properties.

Modules identified in stock data align with known structural features.

Abstract

We address the problem of multiresolution module detection in dense weighted networks, where the modular structure is encoded in the weights rather than topology. We discuss a weighted version of the q-state Potts method, which was originally introduced by Reichardt and Bornholdt. This weighted method can be directly applied to dense networks. We discuss the dependence of the resolution of the method on its tuning parameter and network properties, using sparse and dense weighted networks with built-in modules as example cases. Finally, we apply the method to data on stock price correlations, and show that the resulting modules correspond well to known structural properties of this correlation network.