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UML class diagram of a Graph (abstract data type) The basic operations provided by a graph data structure G usually include: [1] adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y;
Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). 1-planarity [1] 3-dimensional matching [2] [3]: SP1 Bandwidth problem [3]: GT40 Bipartite dimension [3]: GT18
The main alternative to the adjacency list is the adjacency matrix, a matrix whose rows and columns are indexed by vertices and whose cells contain a Boolean value that indicates whether an edge is present between the vertices corresponding to the row and column of the cell. For a sparse graph (one in which most pairs of vertices are not ...
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
In knowledge representation and reasoning, a knowledge graph is a knowledge base that uses a graph-structured data model or topology to represent and operate on data. Knowledge graphs are often used to store interlinked descriptions of entities – objects, events, situations or abstract concepts – while also encoding the free-form semantics ...
A radar chart or "spider chart" or "doi" is a two-dimensional chart of three or more quantitative variables represented on axes starting from the same point. A waterfall chart also known as a "Walk" chart, is a special type of floating-column chart. A tree map where the areas of the rectangles correspond to values. Other dimensions can be ...
They can also provide insight into a data set to help with testing assumptions, model selection and regression model validation, estimator selection, relationship identification, factor effect determination, and outlier detection. In addition, the choice of appropriate statistical graphics can provide a convincing means of communicating the ...
Tanner graphs are partitioned into subcode nodes and digit nodes. For linear block codes, the subcode nodes denote rows of the parity-check matrix H. The digit nodes represent the columns of the matrix H. An edge connects a subcode node to a digit node if a nonzero entry exists in the intersection of the corresponding row and column.