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图的'''<font color="#ff8000">圈空间 Cycle Space</font>'''等j价于其有向关联矩阵的零空间，可以看作是整数或实数或复数上的矩阵。二元循环空间是有向或无向关联矩阵的零空间，也可以看作是二元场上的矩阵。

图的'''<font color="#ff8000">圈空间 Cycle Space</font>'''等j价于其有向关联矩阵的零空间，可以看作是整数或实数或复数上的矩阵。二元循环空间是有向或无向关联矩阵的零空间，也可以看作是二元场上的矩阵。

===Signed and bidirected graphs===

==Signed and bidirected graphs==

The incidence matrix of a [[signed graph]] is a generalization of the oriented incidence matrix. It is the incidence matrix of any [[bidirected graph]] that orients the given signed graph. The column of a positive edge has a 1 in the row corresponding to one endpoint and a −1 in the row corresponding to the other endpoint, just like an edge in an ordinary (unsigned) graph. The column of a negative edge has either a 1 or a −1 in both rows. The line graph and Kirchhoff matrix properties generalize to signed graphs.

The incidence matrix of a [[signed graph]] is a generalization of the oriented incidence matrix. It is the incidence matrix of any [[bidirected graph]] that orients the given signed graph. The column of a positive edge has a 1 in the row corresponding to one endpoint and a −1 in the row corresponding to the other endpoint, just like an edge in an ordinary (unsigned) graph. The column of a negative edge has either a 1 or a −1 in both rows. The line graph and Kirchhoff matrix properties generalize to signed graphs.