Graph Edit Distance Calculator (Heuristic)

This tool calculates an approximate graph edit distance between two randomly generated graphs using a heuristic approach. Graph edit distance is generally an NP-hard problem, meaning exact computation is computationally intensive for large graphs. This heuristic estimates the cost of transforming one graph into another by considering differences in:

• Vertex Label Distribution: Differences in the counts of each unique vertex label between the two graphs.
• Edge Pattern Distribution: Differences in the counts of each unique edge "pattern." An edge pattern is defined by the labels of its two connected vertices (sorted alphabetically) and the edge's own label (e.g., "A-B_X" for an edge between an 'A' and a 'B' vertex with label 'X').

The costs for each elementary operation (vertex/edge insertion or deletion) are predefined as 1 for simplicity. Vertex and edge substitutions are implicitly handled as a deletion of one type and an insertion of another matching type.