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In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is symmetric. The relationship between a graph and the eigenvalues and eigenvectors of its adjacency matrix is studied in spectral graph theory.
PlantUML is an open-source tool allowing users to create diagrams from a plain text language. Besides various UML diagrams, PlantUML has support for various other software development related formats (such as Archimate, Block diagram, BPMN, C4, Computer network diagram, ERD, Gantt chart, Mind map, and WBD), as well as visualisation of JSON and YAML files.
In the case of a graph, the adjacency matrix is a square matrix which indicates whether pairs of vertices are adjacent. Likewise, we can define the adjacency matrix A = ( a i j ) {\displaystyle A=(a_{ij})} for a hypergraph in general where the hyperedges e k ≤ m {\displaystyle e_{k\leq m}} have real weights w e k ∈ R {\displaystyle w_{e_{k ...
Adjacency lists are generally preferred for the representation of sparse graphs, while an adjacency matrix is preferred if the graph is dense; that is, the number of edges | | is close to the number of vertices squared, | |, or if one must be able to quickly look up if there is an edge connecting two vertices.
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In general, a distance matrix is a weighted adjacency matrix of some graph. In a network, a directed graph with weights assigned to the arcs, the distance between two nodes of the network can be defined as the minimum of the sums of the weights on the shortest paths joining the two nodes (where the number of steps in the path is bounded). [2]
A sample DSM with 7 elements and 11 dependency marks. The design structure matrix (DSM; also referred to as dependency structure matrix, dependency structure method, dependency source matrix, problem solving matrix (PSM), incidence matrix, N 2 matrix, interaction matrix, dependency map or design precedence matrix) is a simple, compact and visual representation of a system or project in the ...