Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Spectral Evolution of Social Networks

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

Synonyms

Glossary

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

Spectrum

The set of eigenvalues or singular values of a matrix

Definition

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.

Introduction...

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Notes

Acknowledgments

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