Classification-based prediction of network connectivity robustness.

Today, there is an increasing concern about malicious attacks on various networks in society and industry, against which the network robustness is critical. Network connectivity robustness, in particular, is of fundamental importance, which is generally measured by a sequence of calculated values that indicate the connectedness of the remaining network after a sequence of attacks by means of node- or edge-removal. It is computationally time-consuming, however, to measure and evaluate the network connectivity robustness using the conventional attack simulations, especially for large-scale networked systems. In the present paper, an efficient robustness predictor based on multiple convolutional neural networks (mCNN-RP) is proposed for predicting the network connectivity robustness, which is an natural extension of the single CNN-based predictor. In mCNN-RP, one CNN works as the classifier, while each of the rest CNNs works as an estimator for predicting the connectivity robustness of every classified network category. The network categories are classified according to the available prior knowledge. A data-based filter is installed for predictive data refinement. Extensive experimental studies on both synthetic and real-world networks, including directed and undirected as well as weighted and unweighted topologies, verify the effectiveness of mCNN-RP. The results demonstrate that the average prediction error is lower than the standard deviation of the tested data, which outperforms the single CNN-based framework. The runtime in assessing network connectivity robustness is significantly reduced by using the CNN-based technique. The proposed mCNN-RP not only can accurately predict the connectivity robustness of various complex networks, but also provides an excellent indicator for the connectivity robustness, better than other existing prediction measures.

Evolutionary origin of asymptotically stable consensus.

Consensus is widely observed in nature as well as in society. Up to now, many works have focused on what kind of (and how) isolated single structures lead to consensus, while the dynamics of consensus in interdependent populations remains unclear, although interactive structures are everywhere. For such consensus in interdependent populations, we refer that the fraction of population adopting a specified strategy is the same across different interactive structures. A two-strategy game as a conflict is adopted to explore how natural selection affects the consensus in such interdependent populations. It is shown that when selection is absent, all the consensus states are stable, but none are evolutionarily stable. In other words, the final consensus state can go back and forth from one to another. When selection is present, there is only a small number of stable consensus state which are evolutionarily stable. Our study highlights the importance of evolution on stabilizing consensus in interdependent populations.