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Complex Networks: An Algorithmic Perspective
9.2.3 Hardness of Motif Discovery
There are a number of problems involved in the search of motifs. Firstly, isomorphic
motifs have to be grouped together as they are the occurrences of the same motif.
This process is equivalent to finding the isomorphic subgraphs of a graph which
is a computationally hard problem as we will see in the next section. Secondly, the
number of motifs grows exponentially with the size of the motif. For directed graphs,
there are clearly many more combinations than the undirected motifs of the same
size. We have seen that the number of non-isomorphic motifs of size 3 is tw