Abstract
The functionalities, such as connectivity and communication capability of complex networks, are related to the number and length of paths between node pairs in the networks. In this paper, we propose a new path connectivity measure by considering the number and length of paths of the network (PCNL) to evaluate network path connectivity. By comparing the PCNL with the typical natural connectivity, we prove the effectiveness of the PCNL to measure the path connectivity of networks. Because of the importance of the shortest paths, we further propose the shortest paths connectivity measure (SPCNL) based on the number and length of the shortest paths. Then, we use edge-betweenness-based malicious attacks to study the relationship between the SPCNL and network topology in five types of networks. The results show that the SPCNLs of the networks have a significant corresponding relationship and similar changing trend with their network topology heterogeneities with the increase of the number of deleted edges. These findings mean that the SPCNL is positively correlated with the heterogeneity of the network topology, which provides a new perspective for designing complex networks with high path connectivity.
Highlights
Complex networks such as power grids, transportation networks, and telecommunication networks provide the flow of current, products, and information essential to develop the economy and protect social security
Albert et al [9] studied the changes of the maximal connected component (MCC), i.e., the size of the largest connected subgraph in the remaining network, after a small fraction of the nodes are removed from an exponential network and scale-free network under random attacks and targeted attacks, respectively. ey found that scale-free networks display surprising connectivity against random attacks but are extremely vulnerable to targeted attacks, while the exponential networks do not exhibit this property
We use Monte Carlo simulations to analyze the path connectivity of the above networks and three other types of networks, which are generated from the BA networks by edge rewiring algorithm, against edge-betweenness-based malicious attacks. e results demonstrate that the SPCNL is positively correlated with the heterogeneity of the network topology
Summary
Complex networks such as power grids, transportation networks, and telecommunication networks provide the flow of current, products, and information essential to develop the economy and protect social security. Zeng and Liu [12] proposed a link-robustness index to measure the node connectivity of a network by different malicious attack strategies. Erefore, we propose a new measure (PCNL) in this paper to evaluate the network path connectivity by considering the number and length of the paths. We propose the shortest path connectivity (SPCNL) by only considering the number and length of the shortest paths simultaneously. We use Monte Carlo simulations to analyze the path connectivity of the above networks and three other types of networks, which are generated from the BA networks by edge rewiring algorithm, against edge-betweenness-based malicious attacks.
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