NISQ-ready community detection based on separation-node identification

TL;DR

This paper introduces a quantum computing approach for community detection in networks that uses fewer qubits by identifying separation-nodes, making it more feasible for NISQ devices and large real-world networks.

Contribution

The novel concept of separation-nodes reduces QUBO matrix density, enabling quantum community detection with fewer qubits and improved sparsity compared to existing methods.

Findings

Sparse QUBO matrix achieved through separation-nodes

Greedy heuristic effectively assigns nodes to communities

Proof of concept demonstrated on real-world network data

Abstract

The analysis of network structure is essential to many scientific areas, ranging from biology to sociology. As the computational task of clustering these networks into partitions, i.e., solving the community detection problem, is generally NP-hard, heuristic solutions are indispensable. The exploration of expedient heuristics has led to the development of particularly promising approaches in the emerging technology of quantum computing. Motivated by the substantial hardware demands for all established quantum community detection approaches, we introduce a novel QUBO based approach that only needs number-of-nodes many qubits and is represented by a QUBO-matrix as sparse as the input graph's adjacency matrix. The substantial improvement on the sparsity of the QUBO-matrix, which is typically very dense in related work, is achieved through the novel concept of separation-nodes. Instead of assigning every node to a community directly, this approach relies on the identification of a separation-node set, which -- upon its removal from the graph -- yields a set of connected components, representing the core components of the communities. Employing a greedy heuristic to assign the nodes from the separation-node sets to the identified community cores, subsequent experimental results yield a proof of concept. This work hence displays a promising approach to NISQ ready quantum community detection, catalyzing the application of quantum computers for the network structure analysis of large scale, real world problem instances.