A Briefing Survey on Advances of Coupled Networks With Various Patterns

In real-world scenarios, networks do not exist in isolation but coupled together in different ways, including dependent, multi-support, and inter-connected patterns. And, when a coupled network suffers from structural instability or dynamic perturbations, the system with different coupling patterns shows rich phase transition behaviors. In this review, we present coupled network models with different coupling patterns developed from real scenarios in recent years for studying the system robustness. For the coupled networks with different coupling patterns, based on the network percolation theory, this paper mainly describes the influence of coupling patterns on network robustness. Moreover, for different coupling patterns, we here show readers the research background, research context, and the latest research results and applications. Furthermore, different approaches to improve system robustness with various coupling patterns and future possible research directions for coupled networks are explained and considered.

Network Robustness Analysis Based on Maximum Flow

Network robustness is the ability of a network to maintain a certain level of structural integrity and its original functions after being attacked, and it is the key to whether the damaged network can continue to operate normally. We define two types of robustness evaluation indicators based on network maximum flow: flow capacity robustness, which assesses the ability of the network to resist attack, and flow recovery robustness, which assesses the ability to rebuild the network after an attack on the network. To verify the effectiveness of the robustness indicators proposed in this study, we simulate four typical networks and analyze their robustness, and the results show that a high-density random network is stronger than a low-density network in terms of connectivity and resilience; the growth rate parameter of scale-free network does not have a significant impact on robustness changes in most cases; the greater the average degree of a regular network, the greater the robustness; the robustness of small-world network increases with the increase in the average degree. In addition, there is a critical damage rate (when the node damage rate is less than this critical value, the damaged nodes and edges can almost be completely recovered) when examining flow recovery robustness, and the critical damage rate is around 20%. Flow capacity robustness and flow recovery robustness enrich the network structure indicator system and more comprehensively describe the structural stability of real networks.

Modularity affects the robustness of scale-free model and real-world social networks under betweenness and degree-based node attack

In this paper we investigate how the modularity of model and real-world social networks affect their robustness and the efficacy of node attack (removal) strategies based on node degree (ID) and node betweenness (IB). We build Barabasi–Albert model networks with different modularity by a new ad hoc algorithm that rewire links forming networks with community structure. We traced the network robustness using the largest connected component (LCC). We find that when model networks present absent or low modular structure ID strategy is more effective than IB to decrease the LCC. Conversely, in the case the model network present higher modularity, the IB strategy becomes the most effective to fragment the LCC. In addition, networks with higher modularity present a signature of a 1st order percolation transition and a decrease of the LCC with one or several abrupt changes when nodes are removed, for both strategies; differently, networks with non-modular structure or low modularity show a 2nd order percolation transition networks when nodes are removed. Last, we investigated how the modularity of the network structure evaluated by the modularity indicator (Q) affect the network robustness and the efficacy of the attack strategies in 12 real-world social networks. We found that the modularity Q is negatively correlated with the robustness of the real-world social networks for both the node attack strategies, especially for the IB strategy (p-value < 0.001). This result indicates how real-world networks with higher modularity (i.e. with higher community structure) may be more fragile to node attack. The results presented in this paper unveil the role of modularity and community structure for the robustness of networks and may be useful to select the best node attack strategies in network.

The impact of COVID-19 on the worldwide air transportation network

Air travel has been one of the hardest hit industries of COVID-19, with many flight cancellations and airport closures as a consequence. By analysing structural characteristics of the Official Aviation Guide flight data, we show that this resulted in an increased average distance between airports, and in an increased number of long-range routes. Based on our study of network robustness, we uncover that this disruption is consistent with the impact of a mixture of targeted and random global attack on the worldwide air transportation network. By considering the individual functional evolution of airports, we identify anomalous airports with high centrality but low degree, which further enables us to reveal the underlying transitions among airport-specific representations in terms of both geographical and geopolitical factors. During the evolution of the air transportation network, we also observe how the network attempted to cope by shifting centralities between different airports around the world. Since these shifts are not aligned with optimal strategies for minimizing delays and disconnects, we conclude that they are consistent with politics trumping science from the viewpoint of epidemic containment and transport.

Recovery strategy of multilayer network against cascading failure

Cascading failure phenomena widely exist in real-life circumstances, such as the blackouts in power networks and the collapse in computer networks. In this paper, we construct a cascading failure model on the multilayer network, taking into account the number of invalid neighbors of nodes, the failure frequency of nodes, the effect between layers, and the percolation process. To minimize network losses caused by the cascading process, we propose a recovery strategy, i.e. repairing some certain clusters formed by ineffective nodes and links. The recovery strategy is discussed in detail, like whether to add links to the network, how many links are needed at least to add, how many layers are demanded to restore, and how to choose the values of [Formula: see text] and restorable threshold [Formula: see text] to improve the network performance. Besides, we theoretically analyze the cascading failure model with recovery strategy by virtue of mean-field approximation and generating function techniques. The theoretical solutions are found to be consistent with experimental results simulated on the ER as well as BA networks. In addition, we also investigate the affecting factors of network robustness. The effects of failure threshold [Formula: see text], base number [Formula: see text], and threshold [Formula: see text] between layers on network behaviors depend on the values of average degree [Formula: see text] and recovery proportion [Formula: see text]. These results may provide particular reference significance for maintaining system security, adjusting the network performance, and enhancing network robustness.

Identifying Influential Edges by Node Influence Distribution and Dissimilarity Strategy

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.

The role of evolutionary modes for trait-based cascades in mutualistic networks

The erosion of functional diversity may foster the collapse of ecological systems. Functional diversity is ultimately defined by the distribution of species traits and, as species traits are a legacy of species evolutionary history, one might expect that the mode of trait evolution influence community resistance under the loss of functional diversity. In this paper, we investigate the role of trait evolutionary dynamics on the robustness of mutualistic networks undergoing the following scenarios of species loss: i) random extinctions, ii) loss of functional distinctiveness and iii) biased towards larger trait values. We simulated networks defined by models of single trait complementary and evolutionary modes where traits can arise in recent diversification events with weak phylogenetic signal, in early diversification events with strong phylogenetic signal, or as a random walk through evolutionary time. Our simulations show that mutualistic networks are especially vulnerable to extinctions based on trait distinctiveness and more robust to random extinction dynamics. The networks show intermediate level of robustness against size-based extinctions. Despite the small range of variation in network robustness, our results show that the mode of trait evolution matters for network robustness in all three scenarios. Networks with low phylogenetic signal are more robust than networks with high phylogenetic signal across all scenarios. As a consequence, our results predict that mutualistic networks based upon current adaptations are more likely to cope with extinction dynamics than those networks that are based upon conserved traits.