incidence matrix of a graph in data structure


What is the incidence matrix of a graph?

    The incidence matrixMof the graph Gis an m×nzero-one matrix, with rows indexed by the vertices and columns indexed by the edges, where the entry mijis 1, if the edge ejis incident with the vertex vi,and it is 0 otherwise.

What is the reduced incidence matrix?

    Therefore, the reduced incidence matrix is a square matrix of order n 1; with rank n 1: Thus the result follows. Now a graph G with n vertices and n 1 edges which is not a tree is obviously disconnected.

What are the dimensions of the complete incidence matrix?

    The dimensions of the matrix A is n x b where n is the number of nodes and b is number of branches. For a graph having n nodes and b branches, the complete incidence matrix A is a rectangular matrix of order n x b. In matrix A with n rows and b columns an entry a ij in the i th row and j th column has the following values.

How to use adjacency matrices in the representation of graphs?

    The use of adjacency matrices in the representation of graphs, an alternative method would be the implementation of an adjacency list. An adjacency list is similar to an adjacency matrix in the fact that it is a way of representing a graph, however it uses linked lists to store the connections between nodes.
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