Subgraph centrality in complex networks

2005/04/27 by Ernesto Estrada, Juan A. Rodríguez‐Velázquez, Juan A. Rodriguez-Velazquez · 11 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Adjacency matrix #Artificial intelligence #Betweenness centrality #Bioinformatics and Genomic Networks #Centrality #Closeness #Combinatorics #Complex Network Analysis Techniques #Complex network #Computer science #Data mining #Gene Regulatory Network Analysis #Graph #Mathematics #Measure (data warehouse) #Network analysis #Network science #Network theory #Node (physics) #Physics #Ranking (information retrieval) #Theoretical computer science #cond-mat.stat-mech #physics.soc-ph

paper · pdf · doi:10.1103/physreve.71.056103

published as Physical Review E 71, 056103 (2005) · 29 pages, 4 figures, 2 tables

arxiv created 2005/04/27 · openalex publication_date 2005/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network motifs. We show that the subgraph centrality [C(S)(i)] can be obtained mathematically from the spectra of the adjacency matrix of the network. This measure is better able to discriminate the nodes of a network than alternate measures such as degree, closeness, betweenness, and eigenvector centralities. We study eight real-world networks for which C(S)(i) displays useful and desirable properties, such as clear ranking of nodes and scale-free characteristics. Compared with the number of links per node, the ranking introduced by C(S)(i) (for the nodes in the protein interaction network of S. cereviciae) is more highly correlated with the lethality of individual proteins removed from the proteome.

Citations

• Factoring and weighting approaches to status scores and clique identification
• Community structure in social and biological networks
• Emergence of scaling in random networks
• Eigenvector-centrality — a node-centrality?
• Centrality in social networks conceptual clarification
• Power and Centrality: A Family of Measures
• Statistical mechanics of complex networks
• Evolution of networks
• The large-scale organization of metabolic networks
• The Structure and Function of Complex Networks
• Diameter of the World-Wide Web
• On power-law relationships of the Internet topology
• From the Cover: The structure of scientific collaboration networks

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• Consistency and differences between centrality measures across distinct classes of networks
• Congestion-gradient driven transport on complex networks
• Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network
• Cycle-Centrality in Economic and Biological Networks
• More on the normalized Laplacian Estrada index
• Potential gain as a centrality measure
• Ranking Vertices or Edges of a Network by Loops: A New Approach