The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Analyzing Kleinberg's (and other) small-world Models
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
On the treeness of internet latency and bandwidth
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Dynamics of large networks
The effect of power-law degrees on the navigability of small worlds: [extended abstract]
Proceedings of the 28th ACM symposium on Principles of distributed computing
Greedy forwarding in scale-free networks embedded in hyperbolic metric spaces
ACM SIGMETRICS Performance Evaluation Review
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Realistic, mathematically tractable graph generation and evolution, using kronecker multiplication
PKDD'05 Proceedings of the 9th European conference on Principles and Practice of Knowledge Discovery in Databases
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This paper describes an extension to stochastic Kronecker graphs that provides the special structure required for searchability, by defining a "distance"-dependent Kronecker operator. We show how this extension of Kronecker graphs can generate several existing social network models, such as the Watts-Strogatz small-world model and Kleinberg's lattice-based model. We focus on a specific example of an expanding hypercube, reminiscent of recently proposed social network models based on a hidden hyperbolic metric space, and prove that a greedy forwarding algorithm can find very short paths of length O((log log n)2) for graphs with n nodes.