基于自然连通度的正则图的鲁棒性
Robustness of Regular Graphs Based on Natural Connectivity
摘要：
最近有人提出，自然连通度可以用来有效地刻画复杂网络的鲁棒性。自然连通性通过评估所有长度的闭合行走的加权数量来量化网络中替代路线的冗余度，并且可以被视为从图谱中获得的平均特征值。在本文中，我们探索的自然连通性的规则环格和定期随机图通过度保持随机重布线从定期环格的解析和数值。利用广义Bessel函数重新定义了正则环格的自然连通性，并证明了正则环格的自然连通性与网络规模无关，且随网络规模单调增加.我们还表明，随机正则图具有较低的自然连通性，因此不太强大，比定期环格。
英文摘要：
It has been recently proposed that the natural connectivity can be used to characterize efficiently the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this paper, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalized Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
