# underlying graph

## underlying graph

[¦ən·dər‚lī·iŋ ′graf]
(mathematics)
A directed graph, that results from replacing each directed arc with an undirected edge.
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A simple combinatorial characterization of Markov sources which satisfy this condition is given in terms of cycles of the underlying graph of the Markov chain.
While they are close in size, we observe that the cost of routing over the different graphs is different, and correlated to the underlying graph structure.
It is NP-complete to decide whether an undirected graph G is the underlying graph of an oriented clique.
1) is established on the linearity, it is in fact truly for the linear and non-liner cases because the underlying graph of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]-flow can be decomposed into bouquets and dipoles, hold with conditions of Theorem 4.
alpha]W), where A is the maximum degree of the underlying graph of W.
n] = (G, [micro])), where G = (V, E) is a graph called the underlying graph of [S.
A sigraph is an ordered pair S = (G, [sigma]), where G = (V,E) is a graph called underlying graph of S and [sigma]: E [right arrow] {+, -} is a function.
1) Variations of the graph data structure: The choice of the underlying graph data structure is affected by decisions on the abstract (mathematical) and on the technical level.
Without loss of generality, we assume that the underlying graph is connected so that C(U, [bar]U) [is greater than] 0 for all U.
In our paper we showed that the underlying graph theoretic model of hierarchical opposition is a twin binary tree in which the two 'son' nodes of every 'father' node have the same pair of contrastive labels: pure and impure in the Indian caste system, male and female in Indonesia, and land and noble in Fiji.
The parameter G in the definition of PQ tells LEDA that the underlying graph is G.

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