A graph matching method based on probe assignments

In this paper, a graph matching method and a distance between attributed graphs are defined. Both approaches are based on graph probes. Probes can be seen as features exctracted from a given graph. They represent a local information. According two graphs G1,G2, the univalent mapping can be expresssed as the minimum-weight probe matching between G1 and G2 with respect to the cost function c. 1 Probe Matching and Probe Matching Distance 1.1 Probes of graph Let LV and LE denote the set of node and edge labels, respectively. A labeled, undirected graph G is a 4-tuple G = (V, E, μ, ξ) , where – V is the set of nodes, – E ⊆ V × V is the set of edges – μ : V → LV is a function assigning labels to the nodes, and – ξ : E → LE is a function assigning labels to the edges. From this definition of graph, probes of graph for the matching problem can be expressed as follow: Let G be an attributed graphs with edges labeled from the finite set {l1, l2, ..., a}. Let P be a set of probes extracted from G. There is a probe p for each vertex of the graph G. A probe (p) is defined as a pair < Vi,Hi > where Hi is an edge structure for a given vertex (Vi), Hi is a 2a-tuple of non-negative integers {x1, x2, ..., xa, y1, y2, ..., ya} such that the vertex has exactly xi incoming edges labeled li, and yj outgoing edges labeled lj .