We describe a complete theory for walk-based centrality indices in complex networks defined in terms of Mittag-Leffler functions. This overarching theory includes as special cases well-known centrality measures like subgraph centrality and Katz centrality. The indices we introduce are parametrized by two numbers; by letting these vary, we show that Mittag-Leffler centralities interpolate between degree and eigenvector centrality, as well as between resolvent-based and exponential-based indices. We further discuss modeling and computational issues, and provide guidelines on parameter selection. The theory is then extended to the case of networks that evolve over time. Numerical experiments on synthetic and real-world networks are provided.
翻译:我们描述了在Mittag-Leffler功能定义的复杂网络中基于行走的中心指数的完整理论。这一总体理论包括众所周知的以子集枢和Katz中心等为主的核心衡量标准的特殊案例。我们引入的指数被两个数字相容;如果允许这些差异,我们就表明Mittag-Leffler中心在程度和基因中心之间以及决心和指数基指数之间相互交织。我们进一步讨论了建模和计算问题,并就参数选择提供了指南。然后,该理论扩展至随着时间的推移而演变的网络。提供了合成和现实世界网络的数值实验。