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To obtain the expressions in Table 1, we combine (4) with previously established expressions for G i j on the graphs in question.
These results are likely due to the fact that the graphs in question have significantly more "clique" subgraphs than "dense" or "enriched" subgraphs--as the size of the index grows, so does the potential advantage in using a hierarchical index.
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The graph in question showed the heights of American slaves, servants, soldiers, and apprentices in the early seventeen-hundreds.
We show that a necessary condition for a graph to be equistable is sufficient when the graph in question is distance-hereditary.
The choice of a proper leght of the random walk is important, however, in order to be able to study the local neighborhood of nodes it is necessary and enough to make sure that the chosen number of steps is not too large and that it is smaller than the mixing time in the graph in question, because once the limit of the mixing time is exceeded, our measure will be insensitive to the starting node.
Consequently, it is often not clear which structural features of a graph in question should be taken into account.
More precisely, Trucco [12] and Rashevsky [19] defined entropy measures for graphs which were interpreted as the structural information content of a graph; the original information measure due to Rashevsky [19] is called the so-called topological information of a graph in question, see Equation (4).
We note that even the seemingly most basic of questions, "if L C ( E ) ≅ L C ( F ) as rings, is C ∗ ( E ) ≅ C ∗ ( F ) as C ∗ -algebras?" (and its converse), has only been answered (in the affirmative) for restricted classes of graphs; the question in general remains open (see [18]).
The results revealed a calibration graph for the two powders in question and the compositional variation across the deposit during functionally graded deposition.
After the simulated evidential graphs have been given to the integration method in question the resulting integrated network is evaluated against the original graph.
The differences in the average scores among the major fields of knowledge are clearly shown in the overall average graphs per question (Fig. 2a) within biological sciences (Fig. 2b), exact sciences (Fig. 2c), and human sciences (Fig. 2d) courses.
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