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By Riesen K., Bunke H.

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A graph is termed complete if all pairs of nodes are adjacent. e. the number of incident edges of u. More precisely, the indegree of a node u ∈ V denoted by in(u) and the outdegree of a node u ∈ V denoted by out(u) refers to the number of incoming and outgoing edges of 3 Attributes and attributed graphs are sometimes synonymously used for labels and labeled graphs, respectively. December 28, 2009 18 9:59 Classification and Clustering clustering Graph Classification and Clustering Based on Vector Space Embedding node u, respectively.

Although it is theoretically possible to use different graph matching methods for embedding, the present book is restricted to graph edit distance as the basic dissimilarity model. As a matter of fact, graph edit distance is recognized as one of the most flexible and universal error-tolerant matching paradigms. Particularly, graph edit distance is not restricted to a special class of graphs, but can cope with arbitrary graphs with unconstrained label alphabets for nodes and edges. The next chapter is devoted to a detailed description of graph edit distance and its computation.

Various graph dissimilarity measures can be derived from the maximum common subgraph of two graphs. Intuitively speaking, the larger a maximum common subgraph of two graphs is, the more similar the two graphs are. For instance, in [104] such a distance measure is introduced, defined by dMCS (g1 , g2 ) = 1 − |mcs(g1 , g2 )| max{|g1 |, |g2 |} . Note that, whereas the maximum common subgraph of two graphs is not uniquely defined, the dMCS distance is. If two graphs are isomorphic, their dMCS distance is 0; on the other hand, if two graphs have no part in common, their dMCS distance is 1.

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