# Encyclopedia of Database Systems

Living Edition
| Editors: Ling Liu, M. Tamer Özsu

# Graph Mining on Streams

• Andrew McGregor
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4899-7993-3_184-2

## Definition

Consider a data stream A = 〈 a 1,  a 2,  … ,  a m〉 where each data item a k ∈ [ n] × [ n]. Such a stream naturally defines an undirected, unweighted graph G = ( V, E) where
$$\begin{array}{l}\operatorname{}\operatorname{}\kern1.32em V=\left\{{v}_1,\dots, {v}_n\right\}\; and\\ {}E=\left\{\left({v}_i,{v}_j\right):{a}_k=\left(i,j\right)\kern0.5em \mathrm{for}\;\mathrm{some}\;k\in \left[m\right]\right\}.\end{array}$$
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