Metric in the Set of Labelled Graphs and Its Applications to Network Theory

Yoji KAJITANI; Hidekazu SAKURAI; Eiji OKAMOTO

Metric in the Set of Labelled Graphs and Its Applications to Network Theory

Yoji KAJITANI, Hidekazu SAKURAI, Eiji OKAMOTO

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A concept of metric is defined in the set of labelled graphs. The concept is based on the idea that the extent of the difference in two graphs may be measured by the non-orthogonality of tie-set (loop) vectors of one graph to the cut-set vectors of the other. The meanings involved in the concept are discussed on the topics concerning flow and tension networks. Applications to electrical networks include the theorem that, for a non-reciprocal ⁿ-port network N which is realized by using λ_N controlled-sources, an inequality 1/2 rank (YY^T)D(g_c, g_v)λ_N holds where Y is the admittance matrix of N and D(g_c, g_v) is the distance between the corresponding current graph g_c and voltage graph g_v of N. An example for which the equalities hold in the above inequality is given.

Publication: IEICE TRANSACTIONS on transactions Vol.E59-E No.2 pp.7-12

Publication Date: 1976/02/25

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Type of Manuscript: PAPER

Category: Network Theory

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Yoji KAJITANI
Hidekazu SAKURAI
Eiji OKAMOTO

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Yoji KAJITANI, Hidekazu SAKURAI, Eiji OKAMOTO, "Metric in the Set of Labelled Graphs and Its Applications to Network Theory" in IEICE TRANSACTIONS on transactions, vol. E59-E, no. 2, pp. 7-12, February 1976, doi: .
Abstract: A concept of metric is defined in the set of labelled graphs. The concept is based on the idea that the extent of the difference in two graphs may be measured by the non-orthogonality of tie-set (loop) vectors of one graph to the cut-set vectors of the other. The meanings involved in the concept are discussed on the topics concerning flow and tension networks. Applications to electrical networks include the theorem that, for a non-reciprocal ⁿ-port network N which is realized by using λ_N controlled-sources, an inequality 1/2 rank (YY^T)D(g_c, g_v)λ_N holds where Y is the admittance matrix of N and D(g_c, g_v) is the distance between the corresponding current graph g_c and voltage graph g_v of N. An example for which the equalities hold in the above inequality is given.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e59-e_2_7/_p

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@ARTICLE{e59-e_2_7,
author={Yoji KAJITANI, Hidekazu SAKURAI, Eiji OKAMOTO, },
journal={IEICE TRANSACTIONS on transactions},
title={Metric in the Set of Labelled Graphs and Its Applications to Network Theory},
year={1976},
volume={E59-E},
number={2},
pages={7-12},
abstract={A concept of metric is defined in the set of labelled graphs. The concept is based on the idea that the extent of the difference in two graphs may be measured by the non-orthogonality of tie-set (loop) vectors of one graph to the cut-set vectors of the other. The meanings involved in the concept are discussed on the topics concerning flow and tension networks. Applications to electrical networks include the theorem that, for a non-reciprocal ⁿ-port network N which is realized by using λ_N controlled-sources, an inequality 1/2 rank (YY^T)D(g_c, g_v)λ_N holds where Y is the admittance matrix of N and D(g_c, g_v) is the distance between the corresponding current graph g_c and voltage graph g_v of N. An example for which the equalities hold in the above inequality is given.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Metric in the Set of Labelled Graphs and Its Applications to Network Theory
T2 - IEICE TRANSACTIONS on transactions
SP - 7
EP - 12
AU - Yoji KAJITANI
AU - Hidekazu SAKURAI
AU - Eiji OKAMOTO
PY - 1976
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E59-E
IS - 2
JA - IEICE TRANSACTIONS on transactions
Y1 - February 1976
AB - A concept of metric is defined in the set of labelled graphs. The concept is based on the idea that the extent of the difference in two graphs may be measured by the non-orthogonality of tie-set (loop) vectors of one graph to the cut-set vectors of the other. The meanings involved in the concept are discussed on the topics concerning flow and tension networks. Applications to electrical networks include the theorem that, for a non-reciprocal ⁿ-port network N which is realized by using λ_N controlled-sources, an inequality 1/2 rank (YY^T)D(g_c, g_v)λ_N holds where Y is the admittance matrix of N and D(g_c, g_v) is the distance between the corresponding current graph g_c and voltage graph g_v of N. An example for which the equalities hold in the above inequality is given.
ER -