Geometric randomization of real networks with prescribed degree sequence

Starnini, Michele; Ortiz, Elisenda; Serrano, M. Ángeles

doi:10.1088/1367-2630/ab1e1c

Cited by 5 publications

(5 citation statements)

References 51 publications

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“…( 2) for β ≤ β c . Simulations are performed with the degreepreserving geometric (DPG) Metropolis-Hastings algorithm introduced in 40 , that allows us to explore different values of β while preserving exactly the degree sequence. Given a network, the algorithm selects at random a pair of links connecting nodes i, j and l, m and swaps them (avoiding multiple links and selfconnections) with a probability given by…”

Section: Resultsmentioning

confidence: 99%

An anomalous topological phase transition in spatial random graphs

2022

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Clustering–the tendency for neighbors of nodes to be connected–quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase transition, separating a phase with finite clustering from a regime where clustering vanishes in the thermodynamic limit. We prove this geometric to non-geometric phase transition to be topological in nature, with anomalous features such as diverging entropy as well as atypical finite-size scaling behavior of clustering. Moreover, a slow decay of clustering in the non-geometric phase implies that some real networks with relatively high levels of clustering may be better described in this regime.

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Section: Resultsmentioning

confidence: 99%

An anomalous topological phase transition in spatial random graphs

2022

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“…Actual hidden degrees could be estimated from real data to avoid the mismatch between hidden and observed degrees, but this operation can be demanding and, besides, there is no guarantee that all nodes end up with the exact same degree they had in the real network. An alternative is the implementation of the geometric randomization model introduced in Starnini, Ortiz, and Serrano (2019), which preserves exactly the degree sequence of the input network while producing a version of the network maximally congruent with the S 1 model.…”

Section: A Smentioning

confidence: 99%

The Shortest Path to Network Geometry

Serrano

Boguñá

2021

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Real networks comprise from hundreds to millions of interacting elements and permeate all contexts, from technology to biology to society. All of them display non-trivial connectivity patterns, including the small-world phenomenon, making nodes to be separated by a small number of intermediate links. As a consequence, networks present an apparent lack of metric structure and are difficult to map. Yet, many networks have a hidden geometry that enables meaningful maps in the two-dimensional hyperbolic plane. The discovery of such hidden geometry and the understanding of its role have become fundamental questions in network science giving rise to the field of network geometry. This Element reviews fundamental models and methods for the geometric description of real networks with a focus on applications of real network maps, including decentralized routing protocols, geometric community detection, and the self-similar multiscale unfolding of networks by geometric renormalization.

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“…The GR [58] is a model for the randomization of complex networks with geometric structure, which allows to uniformize their angular coordinate distribution, while preserving the exact degree sequence of the network. It thus applies to both real and synthetic networks where nodes have an observed degree and exist in a similarity space.…”

Section: Geometric Randomization (Gr)mentioning

confidence: 99%

Geometric detection of hierarchical backbones in real networks

Ortiz

García-Pérez

Serrano

2020

Phys. Rev. Research

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Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from treelike structures and the detection of hierarchical ordering remains a challenge, hindered by the small-world property and the presence of a large number of cycles, in particular clustering. Here, we use geometric representations of undirected networks to achieve an enriched interpretation of hierarchy that integrates features defining the popularity of nodes and similarity between them, such that the more similar a node is to a less popular neighbor the higher the hierarchical load of the relationship. The geometric approach allows us to measure the local contribution of nodes and links to the hierarchy within a unified framework. Additionally, we propose a link filtering method, the similarity filter, able to extract hierarchical backbones containing the links that represent statistically significant deviations with respect to the maximum entropy null model for geometric heterogeneous networks. We applied our geometric approach to the detection of similarity backbones of real networks in different domains and found that the backbones preserve local topological features at all scales. Interestingly, we also found that similarity backbones favor cooperation in evolutionary dynamics modeling social dilemmas.

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Geometric randomization of real networks with prescribed degree sequence

Cited by 5 publications

References 51 publications

An anomalous topological phase transition in spatial random graphs

An anomalous topological phase transition in spatial random graphs

The Shortest Path to Network Geometry

Geometric detection of hierarchical backbones in real networks

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