Complete subgraph

A maximal complete subgraph in which every vertex is connected to every other vertex and which is not contained in any other larger subgraph with this property. 

A complete subgraph of a graph is also called a clique. A clique is maximal if it is not contained in any other clique [62]. A maximum clique is the maximal clique with... 

The abstract simplicial complex Cl (G) has various names it is called a flag complex in algebraic topology, while it is called a clique complex in combinatorics, prompted by the fact that clique is another term used in graph theory for complete subgraphs. 

Fig. 1.14 Other CSNs related to that depicted in Fig. 1.7c a simple, complete CSN, b threshold CSN S >0.85) the CSN linking compounds 1 is a complete subgraph/network called a clique, and c threshold CSN (5, >0.90) while compounds 1-4 are still linked they no longer form a elique...

As noted above, the subset of compounds Cpd-l,Cpd-2,Cpd-3,Cpd-4 forms a complete subgraph of the threshold graph called a clique, i.e., Tio gs o.8s- Thus, the four compounds are all hnked in the threshold CSN, while Cpd-5 is an isolated vertex as reflected by the block diagonal stmcture of the adjacency matrix in Eq. (1.57). Because of the block diagonal stmcture, each block can be treated independently of the others, a form of dimensionahty reduction. 

First, for each new reaction (R) added, two generalizations, one very general and one very specific, are calculated. These generalizations (subgraphs) of R will be referred to as the minimum reaction concept (MXC(R)) and the complete reaction concept (CXC(R)), respectively, and are defined as follows ... 

Therefore, searching for some edge-weighted maximal common subgraph for the two complete graphs is equivalent to searching for a clique [58] in this... 

One of the first topologically chiral molecule whose graph contains K5 as a subgraph is probably the completely asymmetric cluster 49 Rh8(CO)19C (Fig. 7) synthesized in 1974 by P. Chini et al. [78]. (Note that the C —Rh bonds are not... 

The other elemental non-trivial graph is Kuratowski s graph K33. K33 is the complete bipartite graph on six vertices, three of which connect to each of the other three. In any object, if one can identify a subgraph K5 or K3 3, then the object is... 

The order of counts is not defined a priori and a subset of relevant subgraph counts can be used instead of the complete SCS. In chemical terms, these subgraphs are recognized as radicals. 

As a whole, the approach based on the decomposition of kinetic graphs into linear and nonlinear subgraphs provides for a complete description of chemical reactions, and at the same time reflects the type and stoichiometry of the nonlinear elementary steps. 

Due to the nature of this approach, subgraph isomorphism algorithms are time consuming isomorphism is a combinatorial problem belonging to the nondetermin-istic polynomial time complete (NP complete) class of problems, which are widely believed to be unsolvable. Several authors suggested improvements to reduce the... 

A graph defined as a subgraph of (7 whose components are K2 (complete graphs) or (cycle graphs) or combinations between a K2 components and b Cm components, under the constraint ... 

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