Complex networks with tuneable dimensions as a universality playground

• URL: http://arxiv.org/abs/2006.10421v3
• Date: Wed, 21 Apr 2021 09:34:47 GMT
• Title: Complex networks with tuneable dimensions as a universality playground
• Authors: Ana P. Mill\'an, Giacomo Gori, Federico Battiston, Tilman Enss, and Nicol\`o Defenu
• Abstract summary: We discuss the role of a fundamental network parameter for universality, the spectral dimension. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from $1$ to infinity. We propose our model as a tool to probe universal behaviour on inhomogeneous structures and comment on the possibility that the universal behaviour of correlated models on such networks mimics the one of continuous field theories in fractional Euclidean dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Universality is one of the key concepts in understanding critical phenomena. However, for interacting inhomogeneous systems described by complex networks a clear understanding of the relevant parameters for universality is still missing. Here we discuss the role of a fundamental network parameter for universality, the spectral dimension. For this purpose, we construct a complex network model where the probability of a bond between two nodes is proportional to a power law of the nodes' distances. By explicit computation we prove that the spectral dimension for this model can be tuned continuously from $1$ to infinity, and we discuss related network connectivity measures. We propose our model as a tool to probe universal behaviour on inhomogeneous structures and comment on the possibility that the universal behaviour of correlated models on such networks mimics the one of continuous field theories in fractional Euclidean dimensions.

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