Decelerated spreading in degree-correlated networks

Role of assortativity in predicting burst synchronization using echo state network

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in the machine's prediction. However, in the case of assortative network, training the machine with the information (i.e., time series) of low degree nodes gives better results in predicting the burst synchronization. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.

Importance of small-degree nodes in assortative networks with degree-weight correlations

It has been known that assortative network structure plays an important role in spreading dynamics for unweighted networks. Yet its influence on weighted networks is not clear, in particular when weight is strongly correlated with the degrees of the nodes as we empirically observed in Twitter. Here we use the self-consistent probability method and revised nonperturbative heterogenous mean-field theory method to investigate this influence on both susceptible-infective-recovered (SIR) and susceptible-infective-susceptible (SIS) spreading dynamics. Both our simulation and theoretical results show that while the critical threshold is not significantly influenced by the assortativity, the prevalence in the supercritical regime shows a crossover under different degree-weight correlations. In particular, unlike the case of random mixing networks, in assortative networks, the negative degree-weight correlation leads to higher prevalence in their spreading beyond the critical transmissivity than that of the positively correlated. In addition, the previously observed inhibition effect on spreading velocity by assortative structure is not apparent in negatively degree-weight correlated networks, while it is enhanced for that of the positively correlated. Detailed investigation into the degree distribution of the infected nodes reveals that small-degree nodes play essential roles in the supercritical phase of both SIR and SIS spreadings. Our results have direct implications in understanding viral information spreading over online social networks and epidemic spreading over contact networks.

Assessing the Influence of an Individual Event in Complex Fault Spreading Network Based on Dynamic Uncertain Causality Graph

Identifying the pivotal causes and highly influential spreaders in fault propagation processes is crucial for improving the maintenance decision making for complex systems under abnormal and emergency situations. A dynamic uncertain causality graph-based method is introduced in this paper to explicitly model the uncertain causalities among system components, identify fault conditions, locate the fault origins, and predict the spreading tendency by means of probabilistic reasoning. A new algorithm is proposed to assess the impacts of an individual event by investigating the corresponding node's time-variant betweenness centrality and the strength of global causal influence in the fault propagation network. The algorithm does not depend on the whole original and static network but on the real-time spreading behaviors and dynamics, which makes the algorithm to be specifically targeted and more efficient. Experiments on both simulated networks and real-world systems demonstrate the accuracy, effectiveness, and comprehensibility of the proposed method for the fault management of power grids and other complex networked systems.

Effects of random rewiring on the degree correlation of scale-free networks

Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature. We comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same. Consequently, the network dynamics is changed, which is proven here by means of the biased random walk.

Predicting the evolution of spreading on complex networks

Due to the wide applications, spreading processes on complex networks have been intensively studied. However, one of the most fundamental problems has not yet been well addressed: predicting the evolution of spreading based on a given snapshot of the propagation on networks. With this problem solved, one can accelerate or slow down the spreading in advance if the predicted propagation result is narrower or wider than expected. In this paper, we propose an iterative algorithm to estimate the infection probability of the spreading process and then apply it to a mean-field approach to predict the spreading coverage. The validation of the method is performed in both artificial and real networks. The results show that our method is accurate in both infection probability estimation and spreading coverage prediction.