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A boolean theory of network flows and metrics and its applications to particle transmission and clustering
Author(s) -
Onaga K.,
Mayeda W.
Publication year - 1979
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.3230090305
Subject(s) - mathematics , boolean network , boolean function , discrete mathematics , complete boolean algebra , parity function , combinatorics , boolean model , cluster (spacecraft) , node (physics) , boolean expression , two element boolean algebra , computer science , algebra over a field , pure mathematics , structural engineering , programming language , filtered algebra , engineering
A network N considered here is a graph (G,E) whose edge e is weighted by I(e) = [α(e), β(e)]. An admissible flow is a flow f satisfying α(e) ⊆ f (e) ⊆ β(e), for all e ⊂ E. A necessary and sufficient condition for existence of admissible Boolean flows in N, and characterization of maximum Boolean flows are presented. Then a property of maximum Boolean flows which are the terminal capacities of two‐terminal Boolean flows satisfy a Boolean triangular inequality is shown. Finally the concept of γ‐relativeness of a symmetric Boolean mapping m for any threshould γ⊆ S which induces a cluster decomposition of the node set V, by introducing Boolean network metrics is presented.