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.

中文翻译：

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测量网络路径连通性的方法

诸如复杂网络的连接性和通信能力之类的功能与网络中节点对之间路径的数量和长度有关。在本文中，我们通过考虑网络路径（PCNL）的数量和长度来评估网络路径连接性，提出了一种新的路径连接性度量。通过将PCNL与典型的自然连通性进行比较，我们证明了PCNL在测量网络路径连通性方面的有效性。由于最短路径的重要性，我们进一步提出了最短路径连接性度量（SPCNL），取决于最短路径的数量和长度。然后，我们使用基于边缘间的恶意攻击来研究五种类型的网络中SPCNL与网络拓扑之间的关系。结果表明，随着删除边数的增加，网络的SPCNL与网络拓扑异质性具有显着的对应关系，并具有相似的变化趋势。这些发现意味着SPCNL与网络拓扑的异质性正相关，这为设计具有高路径连通性的复杂网络提供了新的视角。