Classical and Quantum Random Walks to Identify Leaders in Criminal Networks

TL;DR

This paper explores classical and quantum random walks to identify key leaders in criminal networks, comparing their effectiveness and relationships with network degree in real and synthetic multilayer networks.

Contribution

It introduces new centrality measures based on classical and quantum random walks applied to criminal networks, and compares their performance with synthetic networks.

Findings

Quantum walks provide faster identification of leaders.

Centrality measures correlate with node degree.

Results differ between real and synthetic networks.

Abstract

Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk algorithms provide an exponential speedup over classical algorithms. Classical and quantum random walks can be applied in social network analysis, and can be used to define specific centrality metrics in terms of node occupation on single-layer and multilayer networks. In this paper, we applied these new centrality measures to three real criminal networks derived from an anti-mafia operation named Montagna and a multilayer network derived from them. Our aim is to (i) identify leaders in our criminal networks, (ii) study the dependence between these centralities and the degree, (iii) compare the results obtained for the real multilayer criminal network with those of a synthetic multilayer network which replicates its structure.