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I found that there are algorithms like VFlib and LAD filtering for subgraph isomorphism with one edge type. For multiple node types,one idea could be color all node types with the same type and use colored sub-graph isomorphism which is available for VFlib. I was wondering is there any algo specifically for multiple edge types or should I modify existing algo to check for edge types also?

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You can replace each edge $(u,v)$ with two edges $(u,t_0)$ and $(t_0,v)$ where $t_0$ is a new vertex (a different one for each edge you replace), and then color the vertex $t_0$ based on the type of the edge $(u,v)$.

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