Mathematical Theories of Influencers in Complex Networks

The study of influencers is dovetailed to the big data analysis performed with network theory and artificial intelligence. In a social network (e.g., Twitter, Facebook, Instagram), some individuals spread information more rapidly than any other user. In an epidemic, some individuals are superspreaders who could infect disproportionally many people. In ecosystems, keystone species are responsible for the stability and integrity of the ecological network, analogously to banks that may be too big to fail in an interconnected financial network. Essential genes and neural ensembles in the brain are crucial for integrating information in biological networks. Finding these influencers in a network is crucial to understanding the transference of information and the functionality and resilience of the system, as well as to learning about human behavior and biological function. This chapter discusses the theoretical approaches to understanding, finding, predicting, and creating influencers in general, using theoretical concepts ranging from heuristics and centralities to percolation optimization approaches, spin glasses, and beyond.