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Question: Can a graph be defined in terms of its incidence matrix?

Question:Can a graph be defined in terms of its incidence matrix?

DJJerome1976 540
graphtheory
December 11 2013
0

I would like to define a graph in terms of its incidence matrix. It's very easy to go from the graph to the incidence matrix, but is it possible to go the other way? Here is the incidence matrix of interest:

M:=Matrix([[1,1,0,1,0,0,0],[0,1,1,0,1,0,0],[1,0,1,0,0,1,1],[0,0,0,1,1,1,0],[0,0,0,0,0,0,1]]):
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