Fast algorithm to identify cluster synchrony through fibration symmetries in large information-processing networks

TL;DR

This paper introduces a fast, memory-efficient algorithm for detecting fibration symmetries in large, sparse networks, enabling efficient identification of cluster synchronization patterns related to network functionality.

Contribution

The authors develop a novel, optimized algorithm with $O(M ext{log} N)$ runtime for identifying fibration symmetries, improving upon existing methods especially for large networks.

Findings

Algorithm is suitable for large, sparse networks.

Runtime complexity is $O(M ext{log} N)$.

Provides an optimal method for fiber identification.

Abstract

Recent studies revealed an important interplay between the detailed structure of fibration symmetric circuits and the functionality of biological and non-biological networks within which they have be identified. The presence of these circuits in complex networks are directed related to the phenomenon of cluster synchronization, which produces patterns of synchronized group of nodes. Here we present a fast, and memory efficient, algorithm to identify fibration symmetries over information-processing networks. This algorithm is specially suitable for large and sparse networks since it has runtime of complexity $O(M\log N)$ and requires $O(M+N)$ of memory resources, where $N$ and $M$ are the number of nodes and edges in the network, respectively. We propose a modification on the so-called refinement paradigm to identify circuits symmetrical to information flow (i.e., fibers) by finding the coarsest refinement partition over the network. Finally, we show that the presented algorithm provides an optimal procedure for identifying fibers, overcoming the current approaches used in the literature.