algorithms – subgraph and asymmetric relationship

Lets say we have a network graph G .Take a network that has asymmetric relationships (As in X relates to Y but it does not imply Y relates to X).
Apparently, we can find these networks by finding subgraphs in neighborhoods within the network.
We can find the relationships that correlate to the template. We say a subgraph existts if there is a way to map all the variables in the template to members of the network so the relationships are equivalent

Imagine we are given a network graph G and a neighborhood subgraph Z, how do i find if it is or is not present in the G ?