## Communication, transmission, and transportation networks |

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### Contents

Graphs and Physical Models | 1 |

Definitions and Fundamental Principles | 9 |

Maximum Flow in Deterministic Graphs | 33 |

Copyright | |

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### Common terms and phrases

arbitrary assume assumption augmentation path branch capacities branch flows branch ij branches of G characteristic function columns commodity compute connected Consider the graph constraints contains defined denote directed branches directed graph directed s-t distance matrix element entries equation exists finite flow pattern flow problem function graph G graph in Fig graph shown Hamilton circuit Hence incidence matrix integer Labeling Algorithm least Lemma Let G linear program Max-Flow Min-Cut Theorem maximize maximum flow maximum flow problem median min-cut matrix minimal minimum cost nonnegative normal distribution number of branches number of vertices obtained optimum partitioned Prob probability distribution procedure proved random graph random variable realization s-t cut s-t flow s-t path satisfied Section semigraph Shortest Path shortest tree shown in Fig solution Step subgraph Suppose synthesis terminal capacity matrix triangle inequality undirected vector vertex cut-set vertex vt zero