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Advances in Complex Systems Modelling via Hypergraphs

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

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 7953

Special Issue Editors

Italian National Research Council, Institute of Cognitive Sciences and Technologies (ISTC-CNR), Via San Martino della Battaglia 44, 00185 Rome, Italy
Interests: machine learning; computational intelligence; big data analysis; bioinformatics; computational biology
Special Issues, Collections and Topics in MDPI journals
Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, 00185 Roma, RM, Italy
Interests: soft computing; pattern recognition; computational intelligence; supervised and unsupervised data driven modeling techniques; neural networks; fuzzy systems; evolutionary algorithm
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the last few decades, network science has emerged as a breakthrough field in order to study and investigate complex systems.

A graph (or network) is the archetype of (organized) complexity, where a set of nodes are connected to each other by mutual correlations (edges). Such topological and semantic data structures have been widely used to model telecommunication and computer networks, biological networks and social networks, just to name a few.

However, an intrinsic drawback when dealing with graphs is that they only account for pairwise relationships between nodes; indeed, by definition, an edge can only connect two nodes. This somehow limits the modelling power offered by graphs, yielding an incomplete description of the system under investigation.

Hypergraphs overcome these limitations by allowing hyperedges to connect simultaneously more than two nodes. The greater modelling capabilities of multi-way relationships have been demonstrated in fields such as biology (e.g., protein-protein interaction networks) and social networks (e.g., collaboration networks). Yet the power of hypergraphs is not limited to a mere representation of the data. Hypergraphs and simplicial complexes also play a key role in the emergent field of topological data analysis, whose aim is to analyze a set of data (or point clouds) using techniques derived from topology and mathematics. In fact, rather than analyzing the data itself (which can be difficult due to noise, high-dimensionality, and so on), one can build a filtered set of simplicial complexes and study their properties.

This Special Issue aims to collect high-quality research papers within the research field of hypergraphs, embracing applications, theoretical conceptualizations and computational aspects. Papers bridging the gap between hypergraphs and machine learning are particularly of interest. Position and survey papers are also welcome.

Dr. Alessio Martino
Prof. Dr. Antonello Rizzi
Guest Editors

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

  • Hypergraphs
  • Simplicial Complexes
  • Topological Data Analysis
  • Machine Learning
  • Pattern Recognition
  • Manifold Learning
  • Computational Topology
  • Computational Geometry
  • Persistent Homology
  • Applied Topology
  • Complex Systems

Published Papers (3 papers)

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Research

17 pages, 8869 KiB  
Article
Supply Chain Risk Diffusion in Partially Mapping Double-Layer Hypernetworks
by Ping Yu, Zhiping Wang, Ya’nan Sun and Peiwen Wang
Entropy 2023, 25(5), 747; https://doi.org/10.3390/e25050747 - 02 May 2023
Viewed by 1040
Abstract
The impact of COVID-19 is global, and uncertain information will affect product quality and worker efficiency in the complex supply chain network, thus bringing risks. Aiming at individual heterogeneity, a partial mapping double-layer hypernetwork model is constructed to study the supply chain risk [...] Read more.
The impact of COVID-19 is global, and uncertain information will affect product quality and worker efficiency in the complex supply chain network, thus bringing risks. Aiming at individual heterogeneity, a partial mapping double-layer hypernetwork model is constructed to study the supply chain risk diffusion under uncertain information. Here, we explore the risk diffusion dynamics, drawing on epidemiology, and establish an SPIR (Susceptible–Potential–Infected–Recovered) model to simulate the risk diffusion process. The node represents the enterprise, and hyperedge represents the cooperation among enterprises. The microscopic Markov chain approach (MMCA) is used to prove the theory. Network dynamic evolution includes two removal strategies: (i) removing aging nodes; (ii) removing key nodes. Using Matlab to simulate the model, we found that it is more conducive to market stability to eliminate outdated enterprises than to control key enterprises during risk diffusion. The risk diffusion scale is related to interlayer mapping. Increasing the upper layer mapping rate to strengthen the efforts of official media to issue authoritative information will reduce the infected enterprise number. Reducing the lower layer mapping rate will reduce the misled enterprise number, thereby weakening the efficiency of risk infection. The model is helpful for understanding the risk diffusion characteristics and the importance of online information, and it has guiding significance for supply chain management. Full article
(This article belongs to the Special Issue Advances in Complex Systems Modelling via Hypergraphs)
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20 pages, 890 KiB  
Article
Social Influence Maximization in Hypergraphs
by Alessia Antelmi, Gennaro Cordasco, Carmine Spagnuolo and Przemysław Szufel
Entropy 2021, 23(7), 796; https://doi.org/10.3390/e23070796 - 23 Jun 2021
Cited by 15 | Viewed by 2525
Abstract
This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold [...] Read more.
This work deals with a generalization of the minimum Target Set Selection (TSS) problem, a key algorithmic question in information diffusion research due to its potential commercial value. Firstly proposed by Kempe et al., the TSS problem is based on a linear threshold diffusion model defined on an input graph with node thresholds, quantifying the hardness to influence each node. The goal is to find the smaller set of items that can influence the whole network according to the diffusion model defined. This study generalizes the TSS problem on networks characterized by many-to-many relationships modeled via hypergraphs. Specifically, we introduce a linear threshold diffusion process on such structures, which evolves as follows. Let H=(V,E) be a hypergraph. At the beginning of the process, the nodes in a given set SV are influenced. Then, at each iteration, (i) the influenced hyperedges set is augmented by all edges having a sufficiently large number of influenced nodes; (ii) consequently, the set of influenced nodes is enlarged by all the nodes having a sufficiently large number of already influenced hyperedges. The process ends when no new nodes can be influenced. Exploiting this diffusion model, we define the minimum Target Set Selection problem on hypergraphs (TSSH). Being the problem NP-hard (as it generalizes the TSS problem), we introduce four heuristics and provide an extensive evaluation on real-world networks. Full article
(This article belongs to the Special Issue Advances in Complex Systems Modelling via Hypergraphs)
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21 pages, 1372 KiB  
Article
(Hyper)graph Kernels over Simplicial Complexes
by Alessio Martino and Antonello Rizzi
Entropy 2020, 22(10), 1155; https://doi.org/10.3390/e22101155 - 14 Oct 2020
Cited by 9 | Viewed by 2700
Abstract
Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics [...] Read more.
Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs. Full article
(This article belongs to the Special Issue Advances in Complex Systems Modelling via Hypergraphs)
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