Modelling conflicts with cluster dynamics on networks

TL;DR

This paper models conflicts using cluster dynamics on networks, revealing how action sizes and network evolution influence conflict patterns, with implications for understanding hierarchical structures and long-range correlations in conflict systems.

Contribution

It introduces a novel cluster dynamical model of conflicts on evolving networks, analyzing how network reconstruction affects action size distributions and internal hierarchical structures.

Findings

Action sizes follow a power-law distribution with a non-universal exponent.

Network evolution leads to a hierarchical internal structure with a power-law tail.

Long-range correlations are observed in the temporal patterns of conflicts.

Abstract

We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study the model in its annealed random graph version, on a fixed network, and on a network evolving through the actions. The sizes of actions are distributed with a power-law tail, however, the exponent is non-universal and depends on the frequency of actions and sparseness of the available connections between units. Allowing the network reconstruction over time in a self-organized manner, e.g., by adding the links based on previous liaisons between units, we find that the power-law exponent depends on the evolution time of the network. Its lower limit is given by the universal value 5/2, derived analytically for the case of random fragmentation processes. In the temporal patterns behind the size of actions we find long-range correlations in the time series of number of clusters and non-trivial distribution of time that a unit waits between two actions. In the case of an evolving network the distribution develops a power-law tail, indicating that through the repeated actions, the system develops internal structure which is not just more effective in terms of the size of events, but also has a full hierarchy of units.