# Graph Mining

**DOI:**https://doi.org/10.1007/978-0-387-30164-8_350

## Definition

*Graph Mining* is the set of tools and techniques used to (a) analyze the properties of real-world graphs, (b) predict how the structure and properties of a given graph might affect some application, and (c) develop models that can generate realistic graphs that match the patterns found in real-world graphs of interest.

## Motivation and Background

A graph *G* = (*V*, *E*) consists of a set of edges, *E* connec-ting pairs of nodes from the set *V* ; extensions allow for weights and labels on both nodes and edges. Graphs edges can be used to point *from* one node *to* another, in which case the graph is called directed; in an *undirected* graph, edges must point both ways: *i* → *j* ⇔ *j* → *i*. A variant is the bipartite graph *G* = (*V*_{1}, *V*_{2}, *E*) where only edges linking nodes in *V*_{1} to nodes in *V*_{2} are allowed.

A graph provides a representation of the binary relationships between individual entities, and thus is an extremely common data structure. Examples include the graph of hyperlinks linking HTML...

## References

- Brin, S., & Page, L. (1998). The anatomy of a large-scale hypertextual web search engine.
*Computer Networks and ISDN Systems, 30*(1–7), 107–117.CrossRefGoogle Scholar - Chakrabarti, D., & Faloutsos, C. (2006). Graph mining: Laws, generators and algorithms.
*ACM Computing Surveys, 38*(1).Google Scholar - Kempe, D., Kleinberg, J., & Tardos, E. (2003). Maximizing the spread of influence through a social network. In
*KDD*.Google Scholar - Kuramochi, M., & Karypis, G. (2001). Frequent subgraph discovery. In
*ICDM*(pp. 313–320).Google Scholar - Lovász, L. (1993). Random walks on graphs: A survey. In
*Combinatorics: Paul Erdös is eighty*(Vol. 2, pp. 353–397).Google Scholar - Ng, A., Jordan, M., & Weiss, Y. (2002). On spectral clustering: Analysis and an algorithm. In
*NIPS*.Google Scholar - The structure and function of complex networks. (2003).
*SIAM Review, 45*, 167–256.Google Scholar