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Mathematics
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Structure and Dynamics of Complex Networks
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Structure and Dynamics of Complex Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (31 August 2021) | Viewed by 18459

Special Issue Editor

Dr. Nikita Frolov

E-Mail Website
Guest Editor
Innopolis University, 420500 Innopolis, Russia
Interests: complexity science; network theory; multivariate data processing; brain networks; neuroscience.

Special Issue Information

Dear Colleagues,

Modern network theory provides a universal language to develop relevant models and to analyze the behavior of complex systems. In recent times, a network-theoretical approach has largely contributed to understanding the processes in social, ecological, and biological systems, as well as epidemic spreads, neuronal diseases, and blackouts in power grids.

The aim of this Special Issue is to gather the efforts of experts from various disciplines and to publish original research articles covering advances in the fundamental and applied aspects of structure and dynamics of complex networks. In this framework, diverse emergent phenomena will be discussed, such as explosive synchronization, chimera states, clustering, etc. along with network topology and its statistical properties.

Potential topics include but are not limited to the following:

- Evolving interactions in networks;

- Multilayer networks;

- Explosive synchronization;

- Spatiotemporal coherence and clustering;

- Chimera states;

- Extreme behavior in complex networks;

- Artificial neural networks.

Herewith, I encourage the authors to submit their recent results to this Special Issue to capture state-of-the-art research in the various aspects of complex network theory.

Dr. Nikita Frolov
Guest Editor

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

  • Complex networks
  • Multilayer networks
  • Explosive synchronization
  • Spatio-temporal coherence
  • Clustering
  • Chimera state
  • Extreme events
  • Artificial neural networks

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Published Papers (7 papers)

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Research

23 pages, 1146 KiB  
Article
An Efficient Satellite Resource Cooperative Scheduling Method on Spatial Information Networks
by Huilong Fan, Zhan Yang, Shimin Wu, Xi Zhang, Jun Long and Limin Liu
Mathematics 2021, 9(24), 3293; https://doi.org/10.3390/math9243293 - 17 Dec 2021
Cited by 9 | Viewed by 3797
Abstract
To overcome the low timeliness of resource scheduling problems in spatial information networks, we propose a method based on a dynamic reconstruction of resource request queues and the autonomous coordinated scheduling of resources. First, we construct a small satellite network and combine the [...] Read more.
To overcome the low timeliness of resource scheduling problems in spatial information networks, we propose a method based on a dynamic reconstruction of resource request queues and the autonomous coordinated scheduling of resources. First, we construct a small satellite network and combine the graph maximum flow theory to solve the link resource planning problem during inter-satellite data transmission. In addition, we design a multi-satellite resource scheduling algorithm with minimal time consumption based on graph theory. The algorithm is based on graph theory to reallocate the resource request queue to satellites with idle processing resources. Finally, we simulate the efficient resource scheduling capability in the spatial information network and empirically compare our approaches against two representative swarm intelligence baseline approaches and show that our approach has significant advantages in terms of performance and time consumption during resource scheduling. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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19 pages, 761 KiB  
Article
The Spreading of Shocks in the North America Production Network and Its Relation to the Properties of the Network
by Martha G. Alatriste-Contreras and Martín Puchet Anyul
Mathematics 2021, 9(21), 2795; https://doi.org/10.3390/math9212795 - 4 Nov 2021
Cited by 1 | Viewed by 1907
Abstract
We evaluate the short-run effect of a shock in the manufacturing sector in the North America Production Network. We use input–output data for Canada, Mexico, the USA, and the North America region. With this data we represent the economies as networks and apply [...] Read more.
We evaluate the short-run effect of a shock in the manufacturing sector in the North America Production Network. We use input–output data for Canada, Mexico, the USA, and the North America region. With this data we represent the economies as networks and apply a network diffusion model and execute computer simulations according to different escenarios. We then study the relation between the effects of the shock and the structure of the networks by computing structural properties of sectors. Results show the limited effects of a shock on the manufacturing sector, and thus shed light on the heterogeneous impacts of the trade agreement of the region. They provide useful information to design an industrial policy focused on the development of the production network. In particular, we focus on recommendations for the Mexican economy. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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20 pages, 369 KiB  
Article
Quantifying the Robustness of Complex Networks with Heterogeneous Nodes
by Prasan Ratnayake, Sugandima Weragoda, Janaka Wansapura, Dharshana Kasthurirathna and Mahendra Piraveenan
Mathematics 2021, 9(21), 2769; https://doi.org/10.3390/math9212769 - 1 Nov 2021
Cited by 15 | Viewed by 3000
Abstract
The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous [...] Read more.
The robustness of a complex network measures its ability to withstand random or targeted attacks. Most network robustness measures operate under the assumption that the nodes in a network are homogeneous and abstract. However, most real-world networks consist of nodes that are heterogeneous in nature. In this work, we propose a robustness measure called fitness-incorporated average network efficiency, that attempts to capture the heterogeneity of nodes using the ‘fitness’ of nodes in measuring the robustness of a network. Further, we adopt the same measure to compare the robustness of networks with heterogeneous nodes under varying topologies, such as the scale-free topology or the Erdős–Rényi random topology. We apply the proposed robustness measure using a wireless sensor network simulator to show that it can be effectively used to measure the robustness of a network using a topological approach. We also apply the proposed robustness measure to two real-world networks; namely the CO2 exchange network and an air traffic network. We conclude that with the proposed measure, not only the topological structure, but also the fitness function and the fitness distribution among nodes, should be considered in evaluating the robustness of a complex network. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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16 pages, 755 KiB  
Article
Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons
by Branislav Rehák and Volodymyr Lynnyk
Mathematics 2021, 9(20), 2625; https://doi.org/10.3390/math9202625 - 18 Oct 2021
Cited by 8 | Viewed by 2167
Abstract
An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is [...] Read more.
An algorithm for synchronization of a network composed of interconnected Hindmarsh–Rose neurons is presented. Delays are present in the interconnections of the neurons. Noise is added to the controlled input of the neurons. The synchronization algorithm is designed using convex optimization and is formulated by means of linear matrix inequalities via the stochastic version of the Razumikhin functional. The recovery and the adaptation variables are also synchronized; this is demonstrated with the help of the minimum-phase property of the Hindmarsh–Rose neuron. The results are illustrated by an example. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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13 pages, 440 KiB  
Article
Identifying Influential Edges by Node Influence Distribution and Dissimilarity Strategy
by Yanjie Xu, Tao Ren and Shixiang Sun
Mathematics 2021, 9(20), 2531; https://doi.org/10.3390/math9202531 - 9 Oct 2021
Cited by 1 | Viewed by 2464
Abstract
Identifying influential edges in a complex network is a fundamental topic with a variety of applications. Considering the topological structure of networks, we propose an edge ranking algorithm DID (Dissimilarity Influence Distribution), which is based on node influence distribution and dissimilarity strategy. The [...] Read more.
Identifying influential edges in a complex network is a fundamental topic with a variety of applications. Considering the topological structure of networks, we propose an edge ranking algorithm DID (Dissimilarity Influence Distribution), which is based on node influence distribution and dissimilarity strategy. The effectiveness of the proposed method is evaluated by the network robustness R and the dynamic size of the giant component and compared with well-known existing metrics such as Edge Betweenness index, Degree Product index, Diffusion Intensity and Topological Overlap index in nine real networks and twelve BA networks. Experimental results show the superiority of DID in identifying influential edges. In addition, it is verified through experimental results that the effectiveness of Degree Product and Diffusion Intensity algorithm combined with node dissimilarity strategy has been effectively improved. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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10 pages, 912 KiB  
Article
Identification of Couplings in Adaptive Dynamical Networks of Time-Delayed Feedback Oscillators
by Ilya V. Sysoev, Danil D. Kulminskiy, Vladimir I. Ponomarenko and Mikhail D. Prokhorov
Mathematics 2021, 9(18), 2200; https://doi.org/10.3390/math9182200 - 8 Sep 2021
Viewed by 1498
Abstract
An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction [...] Read more.
An approach to solve the inverse problem of the reconstruction of the network of time-delay oscillators from their time series is proposed and studied in the case of the nonstationary connectivity matrix. Adaptive couplings have not been considered yet for this particular reconstruction problem. The problem of coupling identification is reduced to linear optimization of a specially constructed target function. This function is introduced taking into account the continuity of the nonlinear functions of oscillators and does not exploit the mean squared difference between the model and observed time series. The proposed approach allows us to minimize the number of estimated parameters and gives asymptotically unbiased estimates for a large class of nonlinear functions. The approach efficiency is demonstrated for the network composed of time-delayed feedback oscillators with a random architecture of constant and adaptive couplings in the absence of a priori knowledge about the connectivity structure and its evolution. The proposed technique extends the application area of the considered class of methods. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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10 pages, 884 KiB  
Article
Relay Synchronization in a Weighted Triplex Network
by Md Sayeed Anwar, Dibakar Ghosh and Nikita Frolov
Mathematics 2021, 9(17), 2135; https://doi.org/10.3390/math9172135 - 2 Sep 2021
Cited by 17 | Viewed by 2328
Abstract
Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling [...] Read more.
Relay synchronization in multi-layer networks implies inter-layer synchronization between two indirectly connected layers through a relay layer. In this work, we study the relay synchronization in a three-layer multiplex network by introducing degree-based weighting mechanisms. The mechanism of within-layer connectivity may be hubs-repelling or hubs-attracting whenever low-degree or high-degree nodes receive strong influence. We adjust the remote layers to hubs-attracting coupling, whereas the relay layer may be unweighted, hubs-repelling, or hubs-attracting network. We establish that relay synchronization is improved when the relay layer is hubs-repelling compared to the other cases. We determine analytically necessary stability conditions of relay synchronization state using the master stability function approach. Finally, we explore the relation between synchronization and the topological property of the relay layer. We find that a higher clustering coefficient hinders synchronizability, and vice versa. We also look into the intra-layer synchronization in the proposed weighted triplex network and establish that intra-layer synchronization occurs in a wider range when relay layer is hubs-attracting. Full article
(This article belongs to the Special Issue Structure and Dynamics of Complex Networks)
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