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Models, Topology and Inference of Multilayer and Higher-Order Networks

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (15 September 2023) | Viewed by 8074

Special Issue Editors


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Guest Editor
1. School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
2. The Alan Turing Institute, London NW1 2DB, UK
Interests: statistical mechanics and information theory of networks; multilayer networks; higher-order networks; simplicial complexes; hypergraphs; biological networks

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Guest Editor
1. School of Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, UK
2. The Alan Turing Institute, London NW1 2DB, UK
Interests: network modelling and analysis; multilayer networks; higher-order networks; hypergraphs; applied topology; biological networks

E-Mail Website
Guest Editor
1. School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
2. The Alan Turing Institute, London NW1 2DB, UK
Interests: multilayer networks; higher-order networks; network embedding; random walks; community detection; information theory of networks; biological networks; systems biology

E-Mail Website
Guest Editor Assistant
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK
Interests: percolation theory; higher-order networks; multilayer networks; epidemic spreading; hypergraphs

Special Issue Information

Dear Colleagues,

In recent years, network science has moved from the study of simple networks to the investigation of more complex representations, including multilayer and higher-order structures. These new representations enable researchers to overcome some of the limitations of simple networks by integrating both heterogeneous and higher-order information; consequently, more information can be extracted from data, and the interplay between network structure and dynamics can be more effectively captured. In particular, new perspectives on information theory and inference on networks, combined with network topology and geometry, enable the development of new inference algorithms that offer new ways of analyzing multilayer and higher-order networks. Moreover, going beyond simple pairwise networks is key to revealing important topological and geometrical aspects of dynamical processes and offers a unique opportunity to better understand dynamics on networks. 

Therefore, we welcome contributions including, but not limited to, the following topics:

Multilayer networks
Higher-order networks

Information theory of  networks:
Applied topology
Higher-order network geometry
Higher-order network representation
Multilayer/hypergraph network embedding
Visualization of higher-order networks
Inference algorithms
Community detection 
Bayesian inference
Higher-order/multilayer centrality measures

Dynamical models/higher-order dynamics:
Diffusion models/random walks
Epidemic spreading/contagion 
Percolation models
Synchronization 
Higher-order cascading failure models
Dynamics in the presence of triadic interactions

Prof. Dr. Ginestra Bianconi
Dr. Rubén J. Sánchez-García
Dr. Anthony Baptista
Guest Editors

Hanlin Sun
Guest Editor Assistant

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • information theory of networks
  • Bayesian inference of networks
  • network models
  • network filtering
  • network dynamics
  • higher-order networks
  • multilayer networks
  • topological methods
  • topological signals

Published Papers (6 papers)

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Research

22 pages, 4289 KiB  
Article
What Is in a Simplicial Complex? A Metaplex-Based Approach to Its Structure and Dynamics
by Manuel Miranda, Gissell Estrada-Rodriguez and Ernesto Estrada
Entropy 2023, 25(12), 1599; https://doi.org/10.3390/e25121599 - 29 Nov 2023
Viewed by 1559
Abstract
Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this [...] Read more.
Geometric realization of simplicial complexes makes them a unique representation of complex systems. The existence of local continuous spaces at the simplices level with global discrete connectivity between simplices makes the analysis of dynamical systems on simplicial complexes a challenging problem. In this work, we provide some examples of complex systems in which this representation would be a more appropriate model of real-world phenomena. Here, we generalize the concept of metaplexes to embrace that of geometric simplicial complexes, which also includes the definition of dynamical systems on them. A metaplex is formed by regions of a continuous space of any dimension interconnected by sinks and sources that works controlled by discrete (graph) operators. The definition of simplicial metaplexes given here allows the description of the diffusion dynamics of this system in a way that solves the existing problems with previous models. We make a detailed analysis of the generalities and possible extensions of this model beyond simplicial complexes, e.g., from polytopal and cell complexes to manifold complexes, and apply it to a real-world simplicial complex representing the visual cortex of a macaque. Full article
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18 pages, 2516 KiB  
Article
Cluster Persistence for Weighted Graphs
by Omer Bobrowski and Primoz Skraba
Entropy 2023, 25(12), 1587; https://doi.org/10.3390/e25121587 - 26 Nov 2023
Viewed by 913
Abstract
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology. While this area has been thoroughly studied, we present a new approach to constructing a filtration for cluster analysis via persistent homology. The [...] Read more.
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their 0-dimensional homology. While this area has been thoroughly studied, we present a new approach to constructing a filtration for cluster analysis via persistent homology. The key advantages of the new filtration is that (a) it provides richer signatures for connected components by introducing non-trivial birth times, and (b) it is robust to outliers. The key idea is that nodes are ignored until they belong to sufficiently large clusters. We demonstrate the computational efficiency of our filtration, its practical effectiveness, and explore into its properties when applied to random graphs. Full article
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11 pages, 992 KiB  
Article
Connectivity of Random Geometric Hypergraphs
by Henry-Louis de Kergorlay and Desmond J. Higham
Entropy 2023, 25(11), 1555; https://doi.org/10.3390/e25111555 - 17 Nov 2023
Viewed by 854
Abstract
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how [...] Read more.
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie within a certain radius. From a modelling perspective, we explain how the model captures higher-order connections that arise in real data sets. Our main contribution is to study the connectivity properties of the model. In an asymptotic limit where the number of nodes and hyperedges grow in tandem, we give a condition on the radius that guarantees connectivity. Full article
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16 pages, 1516 KiB  
Article
Robustness and Complexity of Directed and Weighted Metabolic Hypergraphs
by Pietro Traversa, Guilherme Ferraz de Arruda, Alexei Vazquez and Yamir Moreno
Entropy 2023, 25(11), 1537; https://doi.org/10.3390/e25111537 - 11 Nov 2023
Viewed by 1390
Abstract
Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here, we propose a directed hypergraph with edge-dependent vertex weight [...] Read more.
Metabolic networks are probably among the most challenging and important biological networks. Their study provides insight into how biological pathways work and how robust a specific organism is against an environment or therapy. Here, we propose a directed hypergraph with edge-dependent vertex weight as a novel framework to represent metabolic networks. This hypergraph-based representation captures higher-order interactions among metabolites and reactions, as well as the directionalities of reactions and stoichiometric weights, preserving all essential information. Within this framework, we propose the communicability and the search information as metrics to quantify the robustness and complexity of directed hypergraphs. We explore the implications of network directionality on these measures and illustrate a practical example by applying them to a small-scale E. coli core model. Additionally, we compare the robustness and the complexity of 30 different models of metabolism, connecting structural and biological properties. Our findings show that antibiotic resistance is associated with high structural robustness, while the complexity can distinguish between eukaryotic and prokaryotic organisms. Full article
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16 pages, 2515 KiB  
Article
Hyper-Null Models and Their Applications
by Yujie Zeng, Bo Liu, Fang Zhou and Linyuan Lü
Entropy 2023, 25(10), 1390; https://doi.org/10.3390/e25101390 - 28 Sep 2023
Cited by 1 | Viewed by 1183
Abstract
Null models are crucial tools for investigating network topological structures. However, research on null models for higher-order networks is still relatively scarce. In this study, we introduce an innovative method to construct null models for hypergraphs, namely the hyperedge swapping-based method. By preserving [...] Read more.
Null models are crucial tools for investigating network topological structures. However, research on null models for higher-order networks is still relatively scarce. In this study, we introduce an innovative method to construct null models for hypergraphs, namely the hyperedge swapping-based method. By preserving certain network properties while altering others, we generate six hyper-null models with various orders and analyze their interrelationships. To validate our approach, we first employ hypergraph entropy to assess the randomness of these null models across four datasets. Furthermore, we examine the differences in important statistical properties between the various null models and the original networks. Lastly, we investigate the impact of hypergraph randomness on network dynamics using the proposed hyper-null models, focusing on dismantling and epidemic contagion. The findings show that our proposed hyper-null models are applicable to various scenarios. By introducing a comprehensive framework for generating and analyzing hyper-null models, this research opens up avenues for further exploration of the intricacies of network structures and their real-world implications. Full article
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14 pages, 507 KiB  
Article
Distances in Higher-Order Networks and the Metric Structure of Hypergraphs
by Ekaterina Vasilyeva, Miguel Romance, Ivan Samoylenko, Kirill Kovalenko, Daniil Musatov, Andrey Mihailovich Raigorodskii and Stefano Boccaletti
Entropy 2023, 25(6), 923; https://doi.org/10.3390/e25060923 - 12 Jun 2023
Cited by 2 | Viewed by 1454
Abstract
We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, and [...] Read more.
We explore the metric structure of networks with higher-order interactions and introduce a novel definition of distance for hypergraphs that extends the classic methods reported in the literature. The new metric incorporates two critical factors: (1) the inter-node distance within each hyperedge, and (2) the distance between hyperedges in the network. As such, it involves the computation of distances in a weighted line graph of the hypergraph. The approach is illustrated with several ad hoc synthetic hypergraphs, where the structural information unveiled by the novel metric is highlighted. Moreover, the method’s performance and effectiveness are shown through computations on large real-world hypergraphs, which indeed reveal new insights into the structural features of networks beyond pairwise interactions. Namely, using the new distance measure, we generalize the definitions of efficiency, closeness and betweenness centrality for the case of hypergraphs. Comparing the values of these generalized measures with their analogs calculated for the hypergraph clique projections, we show that our measures provide significantly different assessments on the characteristics (and roles) of the nodes from the information-transferability point of view. The difference is brighter for hypergraphs in which hyperedges of large sizes are frequent, and nodes relating to these hyperedges are rarely connected by other hyperedges of smaller sizes. Full article
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