  To measure node importance, network scientists employ centrality scores that
typically take a microscopic or macroscopic perspective, relying on node
features or global network structure. However, traditional centrality measures
such as degree centrality, betweenness centrality, or PageRank neglect the
community structure found in real-world networks. To study node importance
based on network flows from a mesoscopic perspective, we analytically derive a
community-aware information-theoretic centrality score based on network flow
and the coding principles behind the map equation: map equation centrality. Map
equation centrality measures how much further we can compress the network's
modular description by not coding for random walker transitions to the
respective node, using an adapted coding scheme and determining node importance
from a network flow-based point of view. The information-theoretic centrality
measure can be determined from a node's local network context alone because
changes to the coding scheme only affect other nodes in the same module. Map
equation centrality is agnostic to the chosen network flow model and allows
researchers to select the model that best reflects the dynamics of the process
under study. Applied to synthetic networks, we highlight how our approach
enables a more fine-grained differentiation between nodes than node-local or
network-global measures. Predicting influential nodes for two different
dynamical processes on real-world networks with traditional and other
community-aware centrality measures, we find that activating nodes based on map
equation centrality scores tends to create the largest cascades in a linear
threshold model.
