Maximizing synchronizability of duplex networks

Occurrence of super-diffusion in two-layer networks

Super-diffusion is a phenomenon that can be observed in multilayer networks, which describes that the diffusion in a multilayer network is faster than that in the fastest individual layer. In most studies of super-diffusion on two-layer networks, many researchers have focused on the overlap of edges in the two layers and the mode of interlayer connectivity. We discover that the occurrence of super-diffusion in two-layer networks is not necessarily related to the overlap degree. In particular, in a two-layer network, sparse topological structures of individual layers are more beneficial to the occurrence of super-diffusion than dense topological structures. Additionally, similar diffusion abilities of both layers favor super-diffusion. The density of interlayer edges and interlayer connection patterns also influence the occurrence of super-diffusion. This paper offers suggestions to improve the diffusion ability in two-layer networks, which can facilitate the selection of practical information transmission paths between different systems and optimize the design of the internal framework of a company composed of multiple departments.

Maximizing synchronizability of networks with community structure based on node similarity

In reality, numerous networks have a community structure characterized by dense intra-community connections and sparse inter-community connections. In this article, strategies are proposed to enhance synchronizability of such networks by rewiring a certain number of inter-community links, where the research scope is complete synchronization on undirected and diffusively coupled dynamic networks. First, we explore the effect of adding links between unconnected nodes with different similarity levels on network synchronizability and find that preferentially adding links between nodes with lower similarity can improve network synchronizability more than that with higher similarity, where node similarity is measured by our improved Asymmetric Katz (AKatz) and Asymmetric Leicht-Holme-Newman (ALHNII) methods from the perspective of link prediction. Additional simulations demonstrate that the node similarity-based link-addition strategy is more effective in enhancing network synchronizability than the node centrality-based methods. Furthermore, we apply the node similarity-based link-addition or deletion strategy as the valid criteria to the rewiring process of inter-community links and then propose a Node Similarity-Based Rewiring Optimization (NSBRO) algorithm, where the optimization process is realized by a modified simulated annealing technique. Simulations show that our proposed method performs better in optimizing synchronization of such networks compared with other centrality-based heuristic methods. Finally, simulations on the Rössler system indicate that the network structure optimized by the NSBRO algorithm also leads to better synchronizability of coupled oscillators.

A model for analyzing competitive dynamics on triplex networks

This paper studies the evolution process of competitive dynamics on triplex complex networks. We propose a new triplex network model in which the state of the node in each layer is affected by its neighbors as well as inter-layer competition. Through this model, we combine the opinion diffusion model, the Ising model, and the signed network and extend their application from single-layer to multi-layer networks. We derive the evolution process and dynamical equations of the model and carry out a series of numerical simulations to discuss the influence of several factors on the evolution process and the competitiveness of the network. First, we find that the increase of global transition threshold p or the proportion of initial active nodes will lead to more surviving layers and more active nodes in each layer. In addition, we summarize the similarities and differences of the evolution curves under different conditions. Second, we discuss the influence of initial active nodes and the average degree on the competitiveness of the network and find the correlations between them. Finally, we study the relationship between network topology and network competitiveness and conclude the conditions for the best competitiveness of the network. Based on the simulation results, we give specific suggestions on how to improve the competitiveness of the platform in reality.

Synchronizability of two-layer correlation networks

This study investigates the synchronizability of a typical type of two-layer correlation networks formed by two regular networks interconnected with two interlayer linking patterns, namely, positive correlation (PC) and negative correlation (NC). To analyze the network's stability, we consider the analytical expressions of the smallest non-zero and largest eigenvalues of the (weighted) Laplacian matrix as well as the linking strength and the network size for two linking patterns. According to the master stability function, the linking patterns, the linking strength, and the network size associated with two typical synchronized regions exhibit a profound influence on the synchronizability of the two-layer networks. The NC linking pattern displays better synchronizability than the PC linking pattern with the same set of parameters. Furthermore, for the two classical synchronized regions, the networks have optimal intralayer and interlayer linking strengths that maximize the synchronizability while minimizing the required cost. Finally, numerical results verify the validity of the theoretical analyses. The findings based on the representative two-layer correlation networks provide the basis for maximizing the synchronizability of general multiplex correlation networks.

Synchronizability of double-layer dumbbell networks

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers. Furthermore, the largest and smallest nonzero eigenvalues of the Laplacian matrix are calculated analytically and numerically for the single-link coupling pattern and also obtained numerically for the two-link coupling pattern so as to characterize the synchronizability of double-layer dumbbell networks. It is shown that interlayer coupling patterns have a significant impact on the synchronizability of multiplex systems. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis. Our findings can facilitate company managers to select optimal interlayer coupling patterns and to assign proper parameters in terms of improving the efficiency and reducing losses of the whole team.

Optimizing spreading dynamics in interconnected networks

Adding edges between layers of interconnected networks is an important way to optimize the spreading dynamics. While previous studies mostly focused on the case of adding a single edge, the theoretical optimal strategy for adding multiple edges still need to be studied. In this study, based on the susceptible-infected-susceptible model, we investigate the problem of maximizing the stationary spreading prevalence in interconnected networks. For two isolated networks, we maximize the spreading prevalence near the critical point by choosing multiple interconnecting edges. We present a theoretical analysis based on the discrete-time Markov chain approach to derive the approximate optimal strategy. The optimal interlayer structure predicted by the strategy maximizes the spreading prevalence, meanwhile minimizing the spreading outbreak threshold for the interconnected network simultaneously. Numerical simulations on synthetic and real-world networks show that near the critical point, the proposed strategy gives better performance than connecting large degree nodes and randomly connecting.

Optimal interlayer structure for promoting spreading of the susceptible-infected-susceptible model in two-layer networks

Real-world systems, ranging from social and biological to infrastructural, can be modeled by multilayer networks. Promoting spreading dynamics in multilayer networks may significantly facilitate electronic advertising and predicting popular scientific publications. In this study, we propose a strategy for promoting the spreading dynamics of the susceptible-infected-susceptible model by adding one interconnecting edge between two isolated networks. By applying a perturbation method to the discrete Markovian chain approach, we derive an index that estimates the spreading prevalence in the interconnected network. The index can be interpreted as a variant of Katz centrality, where the adjacency matrix is replaced by a weighted matrix with weights depending on the dynamical information of the spreading process. Edges that are less infected at one end and its neighborhood but highly infected at the other will have larger weights. We verify the effectiveness of the proposed strategy on small networks by exhaustively examining all latent edges and demonstrate that performance is optimal or near-optimal. For large synthetic and real-world networks, the proposed method always outperforms other static strategies such as connecting nodes with the highest degree or eigenvector centrality.