Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Semirings and Matrix Analysis of Networks

  • Monika Cerinšek
  • Vladimir Batagelj
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_152

Synonyms

Glossary

Algebraic structure

A set with one or more operations defined on it and rules that hold for them

Network analysis

A study of networks as representations of relations between discrete objects

Sparse matrix

A matrix with most of entries equal to zero

Large network

A network with several thousands or millions of nodes

Complete graph

Kn A graph in which every pair of nodes is linked

Definition

A network can be represented also with a corresponding matrix. Using matrix operations (addition and multiplication) over an appropriate semiring a unified approach to several network analysis problems can be developed. Matrix multiplication is about traveling on network.

Introduction

Semirings are algebraic structures with two operations that provide the basic conditions for studying matrix addition and multiplication and path...

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Notes

Acknowledgments

The first author was financed in part by the European Union, European Social Fund. The work was partially supported by the EUROCORES Programme EUROGIGA of the European Science Foundation, project GReGAS and by Slovenian Research Agency (ARRS) projects J5-5537, J1-6720, and Z7-7614 (B), and grant P1-0294.

References

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Copyright information

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

Authors and Affiliations

  1. 1.Abelium d.o.o, Research and DevelopmentLjubljanaSlovenia
  2. 2.Faculty of Mathematics and Physics, Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  3. 3.Department of Theoretical Computer ScienceInstitute of Mathematics, Physics and MechanicsLjubljanaSlovenia
  4. 4.University of Primorska, Andrej Marušič InstituteKoperSlovenia

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates