Article

Graphs over time: densification laws, shrinking diameters and possible explanations

Authors:

Christos FaloutsosAuthors Info & Claims

KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining

Pages 177 - 187

https://doi.org/10.1145/1081870.1081893

Published: 21 August 2005 Publication History

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 super-linearly 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) or O(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.

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Index Terms

Graphs over time: densification laws, shrinking diameters and possible explanations
1. Information systems
  1. Information systems applications
    1. Data mining

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cover image ACM Conferences

KDD '05: Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining

August 2005

844 pages

ISBN:159593135X

DOI:10.1145/1081870

General Chair:
Robert Grossman
University of Illinois at Chicago & Open Data Partners, USA
,
Program Chairs:
Roberto Bayardo
IBM Almaden Research, USA
,
Kristin Bennett
RPI, USA

Copyright © 2005 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 21 August 2005

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KDD05

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KDD05: The Eleventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

August 21 - 24, 2005

Illinois, Chicago, USA

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Overall Acceptance Rate 1,133 of 8,635 submissions, 13%

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Liu YDu B(2025)Frequency Domain-Oriented Complex Graph Neural Networks for Graph ClassificationIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2024.335176236:2(2733-2746)Online publication date: Feb-2025
https://doi.org/10.1109/TNNLS.2024.3351762
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