Incidence matrix

In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not. There are variations; see below. ( 1 1 1 0 1 0 0 0 0 1 0 1 0 0 1 1 ) . {displaystyle {egin{pmatrix}1&1&1&0\1&0&0&0\0&1&0&1\0&0&1&1\end{pmatrix}}.} In mathematics, an incidence matrix is a matrix that shows the relationship between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The entry in row x and column y is 1 if x and y are related (called incident in this context) and 0 if they are not. There are variations; see below. Incidence matrices are frequently used in graph theory. In graph theory an undirected graph has two kinds of incidence matrices: unoriented and oriented. The unoriented incidence matrix (or simply incidence matrix) of an undirected graph is a n × m matrix B, where n and m are the numbers of vertices and edges respectively, such that Bi,j = 1 if the vertex vi and edge ej are incident and 0 otherwise.