wasserstein distance between two different histograms

I turn a directed labeled graph to histogram. for example if there is one node with label 'a', one with 'b' and two edges between them with label 'x', I turned it to axb and it's value is 2: H('axb')=2. I have some graphs that they belong to same operation but their nodes have different labels (for example if one node belongs to a process in system with pid 100, this process in another graph has different pid) I want to get wasserstein distance between two histograms of graphs. how can I relabel graphs to match? the graphs have not same number of edges even if they are belong to same scenario.