  Random walks on networks is the standard tool for modelling spreading
processes in social and biological systems. This first-order Markov approach is
used in conventional community detection, ranking, and spreading analysis
although it ignores a potentially important feature of the dynamics: where flow
moves to may depend on where it comes from. Here we analyse pathways from
different systems, and while we only observe marginal consequences for disease
spreading, we show that ignoring the effects of second-order Markov dynamics
has important consequences for community detection, ranking, and information
spreading. For example, capturing dynamics with a second-order Markov model
allows us to reveal actual travel patterns in air traffic and to uncover
multidisciplinary journals in scientific communication. These findings were
achieved only by using more available data and making no additional
assumptions, and therefore suggest that accounting for higher-order memory in
network flows can help us better understand how real systems are organized and
function.
