# A mixed-integer linear programming approach for soft graph clustering

## TL;DR

This paper introduces a novel mixed-integer linear programming method for soft graph clustering that allows vertices to belong to multiple clusters with balanced memberships, overcoming limitations of previous approaches.

## Contribution

It is the first approach to simultaneously allocate membership proportions and enforce balanced cluster memberships in soft graph clustering.

## Key findings

- Clusters are not limited to k-clique neighborhoods.
- Method produces non-trivial clusters in connected unweighted graphs.
- Outperforms previous methods in flexibility and applicability.

## Abstract

This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that enforces an equal balance of the cluster memberships. Compared to ([Palla et al., 2005], [Derenyi et al., 2005], [Adamcsek et al., 2006]), the clusters found in our method are not limited to k-clique neighbourhoods. Compared to ([Hope and Keller, 2013]), our method can produce non-trivial clusters even for a connected unweighted graph.