Graph Theory

Mining graph data by Cook D., Holder L. (eds.)

By Cook D., Holder L. (eds.)

This article takes a centred and complete examine mining info represented as a graph, with the newest findings and purposes in either conception and perform supplied. whether you could have minimum heritage in reading graph information, with this publication you’ll have the ability to characterize info as graphs, extract styles and ideas from the information, and practice the methodologies awarded within the textual content to actual datasets.There is a misprint with the hyperlink to the accompanying website for this booklet. For these readers who want to test with the concepts present in this e-book or try out their very own principles on graph facts, the internet web page for the ebook might be http://www.eecs.wsu.edu/MGD.

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As Berendt points out [3], a graph representation of navigation allows the individual’s website roadmap to be constructed. From the graph one can determine which pages act as starting points for the site, which collection of pages are typically navigated sequentially, and how easily (or often) are pages within the site accessed. Navigation graphs can be used to categorize Web surfers and can ultimately assist in organizing websites and ranking Web pages [3, 31, 35, 45]. 3 BOOK OVERVIEW The intention of this book is to provide an overview of the state of the art in mining graph data.

E ⊆ V × V denotes a set of edges. µ : V → LV denotes a node labeling function. ν : E → LE denotes an edge labeling function. The set V can be regarded as a set of node identifiers and is often chosen to be equal to V = {1, . . , |V |}. While V defines the nodes, the set of edges E represents the structure of the graph. That is, a node u ∈ V is connected to a node v ∈ V by an edge e = (u, v) if (u, v) ∈ E. The labeling functions can be used to integrate information about nodes and edges into graphs by assigning attributes from LV and LE to nodes and edges, respectively.

If graph isomorphism is regarded as a formal notion of graph equality, subgraph isomorphism can be seen as subgraph equality. 4 (Subgraph Isomorphism) Let g1 = (V1 , E1 , µ1 , ν1 ) and g2 = (V2 , E2 , µ2 , ν2 ) be graphs. An injective function f : V1 → V2 is called a subgraph isomorphism from g1 to g2 if there exists a subgraph g ⊆ g2 such that f is a graph isomorphism between g1 and g. A subgraph isomorphism exists from g1 to g2 if the larger graph g2 can be turned into a graph that is isomorphic to the smaller graph g1 by removing some nodes and edges.

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