Semirings and Matrix Analysis of Networks
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

K_{n}– 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...
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 J55537, J16720, and Z77614 (B), and grant P10294.
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