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It is against these sets that the graphs of P(C) are contrasted by intersection, i.e. by determining the common graphs between P(C) and (P(g_1)) and between P(C) and (P(g_2)).
(2) Relaxed-graph-cluster contrast: to quantify the presence of the parts of P(C) in (P(D_i)), the parts of (P(D_i)) are expanded into their respective graph partition sets (P(g_1)) and (P(g_2)) (blue) determining the common graphs between P(C) and (P(g_1)) and between P(C) and (P(g_2)), if any.
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The robustness of the most common graph parameters is discussed from Monte Carlo simulations on synthetic graphs.
This is to provide compatibility with the more common graph terminology of vertexes and edges rather than nodes and arcs.
BasicGraph also supplies several convenience member functions that build on the members of Graph for common graph tasks like searching for the existence of a vertex or edge.
There is no common graph in this example, thus (CC_{rg}(C,D_i)=0).
Future work will explore using GraphZIP and its in-memory encoding to speedup common graph algorithms.
The contributions address various issues for knowledge representation and reasoning and the common graph-theoretic background allows to bridge the gap between the different communities.
As shown in Fig. 1 (blue), there is no common graph, the contrast is therefore 0 (blue).
In this paper, we start by providing, in the next section, basic definitions for various common graph theory terms in the context of evolving digraphs.
The first step, which is the monomer search, corresponds to the following two common graph theory problems: "Maximum Common Subgraph" (MCS) problem [15] and "Subgraph Isomorphism" (SI) problem [16].
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