Symmetry in complex networks

DOI10.1016/j.dam.2008.04.008zbMath1168.05058arXiv0705.3215OpenAlexW1992016292MaRDI QIDQ5901448

James W. Anderson, Rubén J. Sánchez-García, Ben D. MacArthur

Publication date: 4 March 2009

Published in: Discrete Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.3215

zbMATH Keywords

symmetryautomorphism groupredundancycomplex network

Mathematics Subject Classification ID

Applications of graph theory (05C90) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (28)

Mathematical frameworks for oscillatory network dynamics in neuroscience ⋮ Controlling consensus in networks with symmetries ⋮ Hidden symmetries in real and theoretical networks ⋮ Equitable decompositions of graphs with symmetries ⋮ Extensions and applications of equitable decompositions for graphs with symmetries ⋮ Concentric network symmetry ⋮ Almost equitable partitions and new necessary conditions for network controllability ⋮ Symmetry-driven network reconstruction through pseudobalanced coloring optimization ⋮ Synchrony in networks of coupled non-smooth dynamical systems: Extending the master stability function ⋮ Relationships between symmetry-based graph measures ⋮ Spectral theory of weighted hypergraphs via tensors ⋮ Communicability cosine distance: similarity and symmetry in graphs/networks ⋮ Finding hidden structures, hierarchies, and cores in networks via isospectral reduction ⋮ Emergence of a spectral gap in a class of random matrices associated with split graphs ⋮ Network-complement transitions, symmetries, and cluster synchronization ⋮ A panoramic sketch about the robust stability of time-delay systems and its applications ⋮ Symmetry in world trade network ⋮ Generating symmetric graphs ⋮ Estimating the effect of the reorganization of interactions on the adaptability of species to changing environments ⋮ General equitable decompositions for graphs with symmetries ⋮ Fourier decompositions of graphs with symmetries and equitable partitions ⋮ The influence of dispersal on a predator-prey system with two habitats ⋮ Algebraic and topological indices of molecular pathway networks in human cancers ⋮ Estimating cellular redundancy in networks of genetic expression ⋮ Koopman operator and its approximations for systems with symmetries ⋮ Characterization of symmetry of complex networks ⋮ Emergence of Balance from a Model of Social Dynamics ⋮ Classical symmetries and the quantum approximate optimization algorithm

Uses Software

• GAP
• Pajek
• BioGRID

Cites Work

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• Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey
• Automorphism groups of Cayley graphs on symmetric groups with generating transposition sets
• Statistical mechanics of complex networks
• Emergence of Scaling in Random Networks
• The probability that a point of a tree is fixed
• The Structure and Function of Complex Networks
• Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks
• Collective dynamics of ‘small-world’ networks
• Exploring complex networks
• Nonlinear dynamics of networks: the groupoid formalism

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