Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations

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Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations (2005)

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by Jure Leskovec , Jon Kleinberg , Christos Faloutsos

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537 - 47 self

BibTeX

@MISC{Leskovec05graphsover,
    author = {Jure Leskovec and Jon Kleinberg and Christos Faloutsos},
    title = { Graphs over Time: Densification Laws, Shrinking Diameters and Possible Explanations},
    year = {2005}
}

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Abstract

How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? Many studies have discovered patterns in static graphs, identifying properties in a single snapshot of a large network, or in a very small number of snapshots; these include heavy tails for in- and out-degree distributions, communities, small-world phenomena, and others. However, given the lack of information about network evolution over long periods, it has been hard to convert these findings into statements about trends over time. Here we study a wide range of real graphs, and we observe some surprising phenomena. First, most of these graphs densify over time, with the number of edges growing superlinearly in the number of nodes. Second, the average distance between nodes often shrinks over time, in contrast to the conventional wisdom that such distance parameters should increase slowly as a function of the number of nodes (like O(log n) orO(log(log n)). Existing graph generation models do not exhibit these types of behavior, even at a qualitative level. We provide a new graph generator, based on a “forest fire” spreading process, that has a simple, intuitive justification, requires very few parameters (like the “flammability” of nodes), and produces graphs exhibiting the full range of properties observed both in prior work and in the present study.

Keyphrases

possible explanation densification law large network heavy tail distance parameter static graph network evolution average distance many study long period surprising phenomenon qualitative level out-degree distribution full range graph generation model real graph small-world phenomenon new graph generator conventional wisdom small number prior work present study forest fire real graph evolve single snapshot normal growth pattern intuitive justification wide range information network

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