极端模网络中的距离分布
Distance Distribution in Extreme Modular Networks
摘要：
模块性是现实世界中大规模复杂网络的一个重要组织原则。许多现实世界的网络呈现出模块化结构，例如交通基础设施、通信网络和社交媒体。在这样的网络中，拥有随机节点对之间的最短路径长度分布（DSPL）的知识对于理解许多过程（包括扩散或流动）非常重要。在这里，我们提供的分析方法，这是在一个极端的模块化结构的大规模网络的模拟很好的协议。极端模块化是指两个模块或社区可以通过最多一个链接连接起来。由于网络的模块化结构，我们得到了一个分布，显示了许多峰值，代表了一个典型的最短路径通过的模块数量。我们目前的理论和结果的情况下，互联链接的加权，以及互联链接的情况下，随机分布在社区中的节点或仅限于一组特定的节点。
英文摘要：
Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge of the shortest paths length distribution (DSPL) between random pairs of nodes in such networks is important for understanding many processes, including diffusion or flow. Here, we provide analytical methods which are in good agreement with simulations on large scale networks with an extreme modular structure. By extreme modular, we mean that two modules or communities may be connected by maximum one link. As a result of the modular structure of the network, we obtain a distribution showing many peaks that represent the number of modules a typical shortest path is passing through. We present theory and results for the case where inter-links are weighted, as well as cases in which the inter-links are spread randomly across nodes in the community or limited to a specific set of nodes.
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