Antisymmetry means the when there is a loop between two node a and b, a must equal b, otherwise it violate the antisymmetry definition.
trail is a sequence of linked edges does not repeat, or [e1,e2…en] in E, where ei !=ej. and e1.node2=e2.node1.
path is a sequence of linked edge does not touch it self.
cycle is a path with two end vertices coincide.
from an adjacency matrix (g) point of view
complete graph is ~diag(ones(1,n)) or 1-diag(ones(1,n))
complement graph is cg=~g
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