Search results
Results From The WOW.Com Content Network
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
The Floyd–Warshall algorithm solves the All-Pair-Shortest-Paths problem for directed graphs. With the adjacency matrix of a graph as input, it calculates shorter paths iterative. After |V | iterations the distance-matrix contains all the shortest paths. The following describes a sequential version of the algorithm in pseudo code:
GraphBLAS (/ ˈ ɡ r æ f ˌ b l ɑː z / ⓘ) is an API specification that defines standard building blocks for graph algorithms in the language of linear algebra. [1] [2] GraphBLAS is built upon the notion that a sparse matrix can be used to represent graphs as either an adjacency matrix or an incidence matrix.
This undirected cyclic graph can be described by the three unordered lists {b, c}, {a, c}, {a, b}. In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph.
The adjacency matrix distributed between multiple processors for parallel Prim's algorithm. In each iteration of the algorithm, every processor updates its part of C by inspecting the row of the newly inserted vertex in its set of columns in the adjacency matrix. The results are then collected and the next vertex to include in the MST is ...
In the example on the left, there are two arrays, C and R. Array C stores the adjacency lists of all nodes. Array R stored the index in C, the entry R[i] points to the beginning index of adjacency lists of vertex i in array C. The CSR is extremely fast because it costs only constant time to access vertex adjacency.
The proof is bijective: a matrix A is an adjacency matrix of a DAG if and only if A + I is a (0,1) matrix with all eigenvalues positive, where I denotes the identity matrix. Because a DAG cannot have self-loops, its adjacency matrix must have a zero diagonal, so adding I preserves the property that all matrix coefficients are 0 or 1. [13]
In algebraic graph theory, the adjacency algebra of a graph G is the algebra of polynomials in the adjacency matrix A(G) of the graph. It is an example of a matrix algebra and is the set of the linear combinations of powers of A. [1] Some other similar mathematical objects are also called "adjacency algebra".