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NodeXL is intended for users with little or no programming experience to allow them to collect, analyze, and visualize a variety of networks. [10] NodeXL integrates into Microsoft Excel 2007, 2010, 2013, 2016, 2019 and 365 and opens as a workbook with a variety of worksheets containing the elements of a graph structure such as
Example graph that has a vertex cover comprising 2 vertices (bottom), but none with fewer. In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem.
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity. Formally, an automorphism of a graph G = ( V , E ) is a permutation σ of the vertex set V , such that the pair of vertices ( u , v ) form an edge if and only if ...
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 ...
The edge-connectivity of a connected vertex-transitive graph is equal to the degree d, while the vertex-connectivity will be at least 2(d + 1)/3. [1] If the degree is 4 or less, or the graph is also edge-transitive, or the graph is a minimal Cayley graph, then the vertex-connectivity will also be equal to d. [4]
A vertex can reach a vertex (and is reachable from ) if there exists a sequence of adjacent vertices (i.e. a walk) which starts with and ends with . In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph.
In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring. Similarly, an edge coloring assigns a color to each edges so that no two adjacent edges are of the same color, and a face coloring of a planar graph assigns a color to each face (or ...
1 V is a vector of |V| ones and A G is the incidence matrix of G, so the third line indicates the constraint that the sum of weights near each vertex is at most 1. Similarly, the minimum fractional vertex-cover size in = (,) is the solution of the following LP: Minimize 1 V · y. Subject to: y ≥ 0 V _____ A G T · y ≥ 1 E.