Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Spectral Evolution of Social Networks

  • Jérôme Kunegis
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_125



Adjacency Matrix

A characteristic matrix of a social network, typically denoted A. If the social network contains n persons, the adjacency matrix is a 0/1 n × n that contains 1 in the entries Aij that correspond to an edge {i, j} and 0 otherwise

Eigenvalue Decomposition

A decomposition of a square matrix giving A = UAUT, in which U contains the eigenvectors of A and Λ contains the eigenvalues

Singular Value Decomposition

A decomposition of any matrix giving A = U∑VT, in which ∑ contains the singular values of A

Spectral Evolution Model

The model that states that over time, eigenvectors stay constant and eigenvalues change


The set of eigenvalues or singular values of a matrix


The term spectral evolution describes a model of the evolution of network based on matrix decompositions. When applied to social networks, this model can be used to predict friendships, recommend friends, and implement other learning problems.


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We thank our collaborators on previous work: Christian Bauckhage, Damien Fay, and Andreas Lommatzsch. The author of this work has received funding from the European Community’s Seventh Frame Programme under grant agreement no 257859, ROBUST.


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Copyright information

© Springer Science+Business Media LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Web Science and TechnologiesUniversity of Koblenz-LandauKoblenzGermany

Section editors and affiliations

  • Thomas Gottron
    • 1
  • Stefan Schlobach
    • 2
  • Steffen Staab
    • 3
  1. 1.Institute for Web Science and TechnologiesUniversität Koblenz-LandauKoblenzGermany
  2. 2.YUAmsterdamThe Netherlands
  3. 3.Institute for Web Science and TechnologiesUniversität Koblenz-LandauKoblenzGermany