Centrality Measures in Complex Networks: A Survey
Akrati Saxena, Sudarshan Iyengar
TL;DR
This survey maps the landscape of node centrality in complex networks, distinguishing local and global measures and surveying their extensions to weighted, directed, multiplex, and dynamic graphs. It covers exact and approximate algorithms, incremental updates, top-k identification, and application-specific centralities, highlighting how different measures capture local versus global influence. The work catalogs methodological advances (e.g., Brandes’ algorithms, harmonic/closeness variants, k-shell decompositions) and practical considerations for large-scale, evolving networks, offering guidance on selecting appropriate measures per context. It also documents real-world applications across domains (air networks, biology, brain, citations, social and urban networks), underscoring the centrality measures’ impact on understanding diffusion, hub formation, and core-periphery structure. Overall, the paper provides a comprehensive reference for researchers and practitioners aiming to quantify node importance in complex, dynamic systems, and it points to open problems and hybrid approaches that tailor centrality to specific networks and tasks.
Abstract
In complex networks, each node has some unique characteristics that define the importance of the node based on the given application-specific context. These characteristics can be identified using various centrality metrics defined in the literature. Some of these centrality measures can be computed using local information of the node, such as degree centrality and semi-local centrality measure. Others use global information of the network like closeness centrality, betweenness centrality, eigenvector centrality, Katz centrality, PageRank, and so on. In this survey, we discuss these centrality measures and the state of the art literature that includes the extension of centrality measures to different types of networks, methods to update centrality values in dynamic networks, methods to identify top-k nodes, approximation algorithms, open research problems related to the domain, and so on. The paper is concluded with a discussion on application specific centrality measures that will help to choose a centrality measure based on the network type and application requirements.