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==Signed and bidirected graphs==

==Signed and bidirected graphs==

'''<font color="#ff8000">有符号双向图 Signed And Bidirected Graphs</font>'''

'''<font color="#ff8000">有符号双向图 Signed And Bidirected Graphs</font>'''<br>

 

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.