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NodeXL is a network analysis and visualization software package for Microsoft Excel 2007/2010/2013/2016. [2] [3] The package is similar to other network visualization tools such as Pajek, UCINet, and Gephi. [4] It is widely applied in ring, mapping of vertex and edge, and customizable visual attributes and tags.
The complete bipartite graph K m,n has a vertex covering number of min{m, n} and an edge covering number of max{m, n}. The complete bipartite graph K m,n has a maximum independent set of size max{m, n}. The adjacency matrix of a complete bipartite graph K m,n has eigenvalues √ nm, − √ nm and 0; with multiplicity 1, 1 and n + m − 2 ...
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A graph is H-free if it does not have an induced subgraph isomorphic to H, that is, if H is a forbidden induced subgraph. The H-free graphs are the family of all graphs (or, often, all finite graphs) that are H-free. [10] For instance the triangle-free graphs are the graphs that do not have a triangle graph as a subgraph.
A graph with 6 vertices and 7 edges where the vertex number 6 on the far-left is a leaf vertex or a pendant vertex. In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph ...
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In that case, one instead evaluates the free energy per vertex in the limit as , where is given by f = − k B T N − 1 log Z . {\displaystyle f=-k_{\rm {B}}TN^{-1}\log Z.} Equivalently, one evaluates the partition function per vertex W {\displaystyle W} in the thermodynamic limit, where
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