Managing and Mining Graph Data part 25 is a comprehensive survey book in graph data analytics. It contains extensive surveys on important graph topics such as graph languages, indexing, clustering, data generation, pattern mining, classification, keyword search, pattern matching, and privacy. It also studies a number of domain-specific scenarios such as stream mining, web graphs, social networks, chemical and biological data. The chapters are written by leading researchers, and provide a broad perspective of the area. This is the first comprehensive survey book in the emerging topic of graph data processing. . | Exact and Inexact Graph Matching Methodology and Applications 223 basic tree search algorithm is endowed with an efficiently computable heuristic which substantially reduces she search terne. In 43 the tree search method lor isomorphism is rped etr by means of another heuristic derived from Constraint Satisfaction. Olficr algorithms l r excel graph matching which are not bated on tree search techniques. are Nauty 150 and detrition tree based techniques 51 to name just two nxampler. The reader is referred to 15 for an eahaustive lisS of iaxetcl. reaph matching algorithms developed since 1973. Closely retated to graph isomocpSiism isa subgraph isomorphism which can be teen as a concept cleecribeng subgraph equality. A subgraph isomorphism is a weaker lotm of matching in terms of reqmsing only that an isomorphism holds bdtween a graph g1 and c iubfraph of g2. Intuí lively subgraph isomorphism is problem to delect I a smaller graph is identically present in a larger graph. lit I ig d esnd c i an example of subgraph isomorphism is given. Definition Subgraph Isomorphism . Let g1 V1 E1 1 1 and g2 V2 be graphs. An injective function f V1 V2 from g1 to g2 is a subgraph isomorphism if there exists a subgraph g C g2 such that f is a graph isomorphism between g1 and g. The tree search based ales lor graph isomorphism 17 43 89 as well as tilts dcclelon trs is based techniques 51 can alao be applied to the subgraph isomosphlem problem. In contraer with problem of graph isomorphism subgraph nomorphism ies known to be NP-complete 25 As a matter of fact suhsraph inomorphism is a havder problem than graph isomorphism as one has nor oniy to chccV whether a pcrmitlalion of g1 is tdsstical Io g2 but we leave to decide whether g1 is iromorehic to any oi the subgraphs of g2 with equal size as gi. The procces of graph metching isriinasíly aims at identifying corresponding suSstrucluscs in tha tw graph under convidcralion. Through the graph .
