Simplicial Complexes and Higher-Order Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (15 May 2023) | Viewed by 1469

Special Issue Editors

Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia
Interests: statistical physics; cooperation; complex systems; evolutionary game theory; network science
Special Issues, Collections and Topics in MDPI journals
Associate Professor of Applied Mathematics, Physics and Applied Mathematics Unit, Indian Statistical, 203 B. T. Road, Kolkata 700108, India
Interests: nonlinear dynamical system; complex networks; chimera state; extreme events; swarmalator

Special Issue Information

Dear Colleagues,

Traditional networks are agglomerates of dyads or pairs that combine to give rise to large, interconnected webs. Although there are numerous paths that can be chosen to form groups out of pairwise connected individuals, the theoretical framework is inherently limited and awkward where it might matter the most, namely when we study group interactions. Indeed, group interactions emerge in a broad variety of social, biological, and technological systems. The remedy is indeed simple but, as past research has already shown, has far reaching consequences. In particular, let the link no longer be bound to connecting just two nodes. By allowing this, we can have links connecting 3, 7, or even 150 nodes all at once. By doing so, we enter into the realm of simplicial complexes and higher-order networks, where 'higher-order' refers to the very fact that links no longer connect just pairs but can directly connect many more nodes of a network. We thus have a theoretical framework to uniquely describe groups by means of a single link, and we can also define the links between different groups or between particular nodes of groups that form the network.

Although the potential impact of simplicial complexes and higher-order networks has already been recognized, interest in these peaked only recently, with mounting inability to converge on what constitutes a group or how to consistently define it in the realm of traditional network science. This ineptitude comes to a head when we study peer pressure, public cooperation, complex contagion, or opinion formation, to name just some examples that clearly extend well beyond pairwise interactions. More generally, however, almost every human interaction sometimes involves more than two people, thus creating an inherent need for the introduction of higher-order structures. Although past research has often successfully leveraged the language of pairwise networks to describe higher-order interactions, a paradigm shift in the way we model interactions in groups is well under way. We therefore believe that the timing of this Special Issue dedicated to simplicial complexes and higher-order networks is perfect, and we hope to receive many interesting contributions on topics such as:

  • Diffusion of information
  • Dismantling and immunization
  • Trust, trustworthiness, and honesty
  • Evolution of cooperation
  • Trust and ultimatums
  • Epidemic spreading
  • Opinion formation
  • Peer pressure

Prof. Dr. Matjaz Perc
Dr. Dibakar Ghosh
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. Mathematics is an international peer-reviewed open access semimonthly 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

  • diffusion of information
  • dismantling and immunization
  • trust, trustworthiness, and honesty
  • evolution of cooperation
  • trust and ultimatums
  • epidemic spreading
  • opinion formation
  • peer pressure

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

18 pages, 4310 KiB  
Article
The Impact of Higher-Order Interactions on the Synchronization of Hindmarsh–Rose Neuron Maps under Different Coupling Functions
by Mahtab Mehrabbeik, Atefeh Ahmadi, Fatemeh Bakouie, Amir Homayoun Jafari, Sajad Jafari and Dibakar Ghosh
Mathematics 2023, 11(13), 2811; https://doi.org/10.3390/math11132811 - 22 Jun 2023
Cited by 5 | Viewed by 788
Abstract
In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The [...] Read more.
In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh–Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as two- and three-body interactions in three homogeneous and two heterogeneous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths. Full article
(This article belongs to the Special Issue Simplicial Complexes and Higher-Order Networks)
Show Figures

Figure 1

Back to TopTop