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

@inproceedings{Leskovec2005GraphsOT,
  title={Graphs over time: densification laws, shrinking diameters and possible explanations},
  author={Jure Leskovec and Jon M. Kleinberg and Christos Faloutsos},
  booktitle={KDD '05},
  year={2005}
}
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… Expand
Graphs Over Time: Densification and Shrinking Diameters
TLDR
A new graph generator, based on a “forest fire” spreading process, is provided that has a simple, intuitive justification, requires very few parameters, and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. Expand
Laws of Graph Evolution: Densification and Shrinking Diameters
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, identifyingExpand
Graph evolution: Densification and shrinking diameters
TLDR
A new graph generator is provided, based on a forest fire spreading process that has a simple, intuitive justification, requires very few parameters, and produces graphs exhibiting the full range of properties observed both in prior work and in the present study. Expand
Densification arising from sampling fixed graphs
TLDR
The proposed Edge Sampling model possesses several interesting features, in particular, that edges and nodes discovered can exhibit densification, and it is shown that the node degree of the fixed underlying graph follows a heavy-tailed distribution can yield power law densification. Expand
Affiliation networks
TLDR
This paper presents the first model that provides a simple, realistic, and mathematically tractable generative model that intrinsically explains all the well-known properties of the social networks, as well as densification and shrinking diameter. Expand
Weighted graphs and disconnected components: patterns and a generator
TLDR
This work observes that the non-giant connected components seem to stabilize in size, and proposes an intuitive, generative model for graph growth that obeys observed patterns. Expand
Weighted Graphs and Disconnected Components
The vast majority of earlier work has focused on graphs which are both connected (typically by ignoring all but the giant connected component), and unweighted. Here we study numerous, real, weightedExpand
Dynamics of Real-world Networks
In our recent work we found very interesting and unintuitive patterns for time evolving networks, which change some of the basic assumptions that were made in the past. The main objective ofExpand
Graph mining: Laws, generators, and algorithms
TLDR
This survey gives an overview of the incredible variety of work that has been done on graph problems and one of the main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Expand
Structural sparseness and complex networks
  • F. Reidl
  • Computer Science, Mathematics
  • 2016
TLDR
It is stated that the theory of structurally sparse graphs is applicable to complex networks and, as a corollary, so is the rich algorithmic toolkit it provides and several fundamental network models exhibit these properties. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 34 REFERENCES
The Web as a Graph: Measurements, Models, and Methods
TLDR
This paper describes two algorithms that operate on the Web graph, addressing problems from Web search and automatic community discovery, and proposes a new family of random graph models that point to a rich new sub-field of the study of random graphs, and raises questions about the analysis of graph algorithms on the Internet. Expand
The average distances in random graphs with given expected degrees
  • F. Chung, L. Lu
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 2002
TLDR
It is shown that for certain families of random graphs with given expected degrees the average distance is almost surely of order log n/log d́, where d̃ is the weighted average of the sum of squares of the expected degrees. Expand
R-MAT: A Recursive Model for Graph Mining
TLDR
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 is proposed. Expand
Collective dynamics of ‘small-world’ networks
TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. Expand
Stochastic models for the Web graph
TLDR
The results are two fold: it is shown that graphs generated using the proposed random graph models exhibit the statistics observed on the Web graph, and additionally, that natural graph models proposed earlier do not exhibit them. Expand
The Diameter of a Scale-Free Random Graph
We consider a random graph process in which vertices are added to the graph one at a time and joined to a fixed number m of earlier vertices, where each earlier vertex is chosen with probabilityExpand
ANF: a fast and scalable tool for data mining in massive graphs
Graphs are an increasingly important data source, with such important graphs as the Internet and the Web. Other familiar graphs include CAD circuits, phone records, gene sequences, city streets,Expand
Emergence of scaling in random networks
TLDR
A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems. Expand
Small-World Phenomena and the Dynamics of Information
TLDR
It is found that short chains are pervasive, and that people are able to find them, and this latter point is concerned precisely with a type of decentralized navigation in a social network, consisting of people as nodes and links joining. Expand
The Structure and Function of Complex Networks
  • M. Newman
  • Physics, Computer Science
  • SIAM Rev.
  • 2003
TLDR
Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks. Expand
...
1
2
3
4
...