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 函数定义的复杂网络中以步行为基础的中心指数的完整理论,这一总体理论包括作为特殊案例的众所周知的中心指标,如子中央和Katz中心。我们引入的指数被两个数字相容;我们让这些不同数字来显示Mittag-Leffler中心在程度和能量中心之间以及决心中心与指数性指数之间相互交织。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,该理论扩大到了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。