## R-MAT: A recursive model for graph mining (2004)

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Venue: | In Fourth SIAM International Conference on Data Mining (SDM’ 04 |

Citations: | 151 - 17 self |

### BibTeX

@INPROCEEDINGS{Chakrabarti04r-mat:a,

author = {Deepayan Chakrabarti and Yiping Zhan and Christos Faloutsos},

title = {R-MAT: A recursive model for graph mining},

booktitle = {In Fourth SIAM International Conference on Data Mining (SDM’ 04},

year = {2004}

}

### Years of Citing Articles

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### Abstract

How does a ‘normal ’ computer (or social) network look like? How can we spot ‘abnormal ’ sub-networks in the Internet, or web graph? The answer to such questions is vital for outlier detection (terrorist networks, or illegal money-laundering rings), forecasting, and simulations (“how will a computer virus spread?”). The heart of the problem is finding the properties of real graphs that seem to persist over multiple disciplines. We list such “laws ” and, more importantly, we propose a simple, parsimonious model, the “recursive matrix ” (R-MAT) model, which can quickly generate realistic graphs, capturing the essence of each graph in only a few parameters. Contrary to existing generators, our model can trivially generate weighted, directed and bipartite graphs; it subsumes the celebrated Erdős-Rényi model as a special case; it can match the power law behaviors, as well as the deviations from them (like the “winner does not take it all ” model of Pennock et al. [21]). We present results on multiple, large real graphs, where we show that our parameter fitting algorithm (AutoMAT-fast) fits them very well. 1

### Citations

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Citation Context ...nt graph generators can be grouped in two classes: degree based and procedural. Given a degree distribution (typically following a power-law), the degreebased ones try to find a graph that matches it =-=[2, 17]-=-, but without giving any insights about the graph or trying to match other criteria (like small diameter, eigenvalues etc.). On the other hand, procedural generators try to find simple mechanisms to g... |

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Citation Context ...s, networks and their surprising regularities/laws have been attracting significant interest recently. The World Wide Web, the Internet topology and Peer-toPeer networks follows surprising power-laws =-=[5, 10, 3]-=-, exhibit strange “bow-tie” or “jellyfish” structures [5, 23], while still having a small diameter [2]. Finding patterns, laws and regularities in large real networks has numerous applications, from c... |

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Citation Context ... subsumes the celebrated Erdős-Rényi model as a special case; it can match the power law behaviors, as well as the deviations from them (like the “winner does not take it all” model of Pennock et al. =-=[20]-=-). We present results on multiple, large real graphs, where we show that our parameter fitting algorithm (AutoMAT-fast) fits them very well. 1 Introduction Graphs, networks and their surprising regula... |

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Citation Context ...er duplicate elimination (a, b, c, d) Probabilities of an edge falling into partitions in the R-MAT model. a + b + c + d = 1. Table 1: Table of Symbols generators have been proposed in passing before =-=[19]-=-, but the emphasis was on network issues. 3.1 Fast Algorithm to generate Directed Graphs: The adjacency matrix A of a graph of N nodes is an N ∗ N matrix, with entry a(i, j) = 1 if the edge (i, j) exi... |

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Citation Context ...hool of Computer Science, CMU ‡School of Computer Science, CMU This is exactly the main part of this work. We propose the Recursive Matrix (R-MAT) model, which naturally generates power-law (or “DGX” =-=[4]-=- ) degree distributions. We show that it naturally leads to smallworld graphs; it is recursive (=self-similar), and it has only a small number of parameters. The rest of this paper is organized as fol... |

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Citation Context ...“jellyfish” structures [5, 23], while still having a small diameter [2]. Finding patterns, laws and regularities in large real networks has numerous applications, from criminology and law enforcement =-=[8]-=- to analyzing virus propagation patterns [19]and understanding networks of regulatory genes and interacting proteins [3] and so on. Discovering and listing such laws is only the first step. Ideally, w... |

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Citation Context ...s, networks and their surprising regularities/laws have been attracting significant interest recently. The World Wide Web, the Internet topology and Peer-toPeer networks follows surprising power-laws =-=[5, 10, 3]-=-, exhibit strange “bow-tie” or “jellyfish” structures [5, 24], while still having a small diameter [2]. Finding patterns, laws and regularities in large real networks has numerous applications, from c... |

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Topology of complex networks: Local events and universality
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Citation Context ...wever, this only gives power laws of exponent 3. Many modifications and alternatives to the basic idea have been proposed; some generators also include the geometrical layout of nodes in their models =-=[1, 2, 17, 20, 6]-=-. The BRITE graph generator [15] uses components from several of the above models. In general, all of the above generators fail to meet one or more of the following goals: (a) the generator should be ... |