“adjacency matrix”的概念、定义、翻译、参考文献-科学参考

adjacency matrix

Mathematics

For a graph G, with n vertices v₁, v₂,…, v_n, the adjacency matrix A is the n×n matrix [a_ij] with a_ij equalling the number of edges connecting v_i to v_j. The matrix A is symmetric if G is not directed and the sum of any row’s (or column’s) entries is equal to the degree of the corresponding vertex. An example of a graph and its adjacency matrix A is shown in the figure.

A graph G

The adjacency matrix of G

Computer

A matrix used as a means of representing an adjacency structure, which in turn represents a graph. If A is the adjacency matrix corresponding to a given graph G, then
$a_{i j} = 1$
if there is an edge from vertex i to vertex j in G; otherwise
$a_{i j} = 0$
If G is a directed graph then
$a_{i j} = 1$
if there is an edge directed from vertex i to vertex j; otherwise
$a_{i j} = 0$
If the vertices of the graph are numbered 1,2,…m, the adjacency matrix is of a type m×m. If
$A \times A \times \dots \times A (p terms, p \leq m)$
is evaluated, the nonzero entries indicate those vertices that are joined by a path of length p; indeed the value of the (i,j)th entry of A^p gives the number of paths of length p from the vertex i to vertex j. By examining the set of such matrices,
$p = 1, 2, \dots, m - 1$
it can be determined whether two vertices are connected.
It is also possible for adjacency matrices to be formed from Boolean matrices.

单词	adjacency matrix
释义	adjacency matrix Mathematics For a graph G, with n vertices v₁, v₂,…, v_n, the adjacency matrix A is the n×n matrix [a_ij] with a_ij equalling the number of edges connecting v_i to v_j. The matrix A is symmetric if G is not directed and the sum of any row’s (or column’s) entries is equal to the degree of the corresponding vertex. An example of a graph and its adjacency matrix A is shown in the figure. A graph G The adjacency matrix of G Computer A matrix used as a means of representing an adjacency structure, which in turn represents a graph. If A is the adjacency matrix corresponding to a given graph G, then $a_{i j} = 1$ if there is an edge from vertex i to vertex j in G; otherwise $a_{i j} = 0$ If G is a directed graph then $a_{i j} = 1$ if there is an edge directed from vertex i to vertex j; otherwise $a_{i j} = 0$ If the vertices of the graph are numbered 1,2,…m, the adjacency matrix is of a type m×m. If $A \times A \times \dots \times A (p terms, p \leq m)$ is evaluated, the nonzero entries indicate those vertices that are joined by a path of length p; indeed the value of the (i,j)th entry of A^p gives the number of paths of length p from the vertex i to vertex j. By examining the set of such matrices, $p = 1, 2, \dots, m - 1$ it can be determined whether two vertices are connected. It is also possible for adjacency matrices to be formed from Boolean matrices.
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