Paper（2004）：Thirty years of graph matching in pattern recognition

1.The category of graph matching

1.1 Exact matching algorithms

Exact matching algorithm:should be edge-preserving,which means if 2 nodes in the first graph are linked by an edge, they are mapped to 2nodes in the second graph that are linked to an edge as well.

graph isomorphism:a one-to-one correspondence must be found between each node of the first graph and each node of the second graph.

subgraph isomorphism: an isomorphism holds between one of the two graphs and a node-induced subgraph of the other.

monomorphism:each node of the first graph is mapped to a distinct node of the second one,and each edge of the first graph has a corresponding edge in the second one; the second graph, however, may have both extra nodes and extra edges.

homomorphisim:nodes in the first graph are to be mapped to distinct nodes of the other,many-to-one.

maximum common subgraph(MCS): map a subgraph of the first graph to an isomorphic subgraph of the second one.

2.The application of the graph matching

Graph Matching(一)