  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.
