Graph evolution: Densification and shrinking diameters

@article{Leskovec2007GraphED,
  title={Graph evolution: Densification and shrinking diameters},
  author={Jure Leskovec and Jon M. Kleinberg and Christos Faloutsos},
  journal={ACM Trans. Knowl. Discov. Data},
  year={2007},
  volume={1},
  pages={2}
}
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

Paper Mentions

Blog Post
The Many Faces of Graph Dynamics
TLDR
The notion of centrality distance, a natural similarity measure for two graphs which depends on a given centrality, characterizing the graph type, is introduced, which allows us to compare the dynamics of very different networks, in terms of scale and evolution speed. 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
The rise and fall of network stars: Analyzing 2.5 million graphs to reveal how high-degree vertices emerge over time
TLDR
A flexible network-generation model is developed based on large-scale, real-world data that gives a better understanding of how stars rise and fall within networks, and is applicable to dynamic systems both in nature and society. Expand
Non-altering time scales for aggregation of dynamic networks into series of graphs
TLDR
This work addresses the fundamental question of knowing whether a series of graphs formed using a given Δ faithfully describes the original link stream by designing an automatic method to determine the saturation scale of any link stream, which is applied and validate on several real-world datasets. Expand
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
Non-altering time scales for aggregation of dynamic networks into series of graphs
TLDR
This work addresses the fundamental question of knowing whether a series of graphs formed using a given Δ faithfully describes the original link stream by showing that such dynamic networks exhibit a threshold for Δ, which it is shown is the saturation scale. Expand
Modeling the Evolution of Networks as Shrinking Structural Diversity
TLDR
It is shown that most numerical network characteristics follow statistically significant trends going either up or down, and that these trends can be predicted by considering the notion of diversity. Expand
Estimating robustness in large social graphs
TLDR
A measure that characterizes the robustness properties of a graph and also serves as global measure of the community structure (or lack thereof) is presented and how to compute this measure efficiently is shown, by exploiting the special spectral properties of real-world networks. Expand
Diameter and Rumour Spreading in Real-World Network Models
The so-called ‘small-world phenomenon’, observed in many real-world networks, is that there is a short path between any two nodes of a network, whose length is much smaller that the network’s size,Expand
On Power Law Growth of Social Networks
TLDR
For the first time, this work examines the growth of WeChat, which is the largest online social network in China, together with several other real social networks, and proposes NetTide, a model that encompasses many traditional growth dynamics as special cases, while remaining parsimonious in parameters. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 64 REFERENCES
Graphs over time: densification laws, shrinking diameters and possible explanations
TLDR
A new graph generator is provided, 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. Expand
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
Sampling from large graphs
TLDR
The best performing methods are the ones based on random-walks and "forest fire"; they match very accurately both static as well as evolutionary graph patterns, with sample sizes down to about 15% of the original graph. Expand
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
Organization of growing random networks.
  • P. Krapivsky, S. Redner
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2001
TLDR
The organizational development of growing random networks is investigated, and the combined age and degree distribution of nodes shows that old nodes typically have a large degree. 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
Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications
TLDR
This paper introduces a structural metric that allows us to differentiate between all simple, connected graphs having an identical degree sequence, which is of particular interest when that sequence satisfies a power law relationship. 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
Network growth by copying.
  • P. Krapivsky, S. Redner
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
TLDR
A growing network model in which a new node attaches to a randomly selected node, as well as to all ancestors of the target node, produces a sparse, ultrasmall network where the average node degree grows logarithmically with network size while the network diameter equals 2. Expand
Accelerated growth of networks
TLDR
It is shown that the accelerated growth of networks fairly well explains the structure of the Word Web (the network of interacting words of human language) and is used to describe a wealth condensation transition in evolving societies. Expand
...
1
2
3
4
5
...