A trade-off between space and efficiency for routing tables
Journal of the ACM (JACM)
On sparse spanners of weighted graphs
Discrete & Computational Geometry
On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Proceedings of the 9th international World Wide Web conference on Computer networks : the international journal of computer and telecommunications netowrking
The degree sequence of a scale-free random graph process
Random Structures & Algorithms
Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Random Structures & Algorithms
Stochastic models for the Web graph
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Random Evolution in Massive Graphs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
The Diameter of a Scale-Free Random Graph
Combinatorica
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Microscopic evolution of social networks
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
A simple linear time algorithm for computing a (2k - 1)-spanner of o(n1+1/k) size in weighted graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
A social network based study of software team dynamics
Proceedings of the 3rd India software engineering conference
Evolution of developer collaboration on the jazz platform: a study of a large scale agile project
Proceedings of the 4th India Software Engineering Conference
Milgram-routing in social networks
Proceedings of the 20th international conference on World wide web
Data generation using declarative constraints
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Modeling social networks through user background and behavior
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
Automatic text summarization and small-world networks
Proceedings of the 11th ACM symposium on Document engineering
A clustering coefficient network formation game
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Finding overlapping communities in social networks: toward a rigorous approach
Proceedings of the 13th ACM Conference on Electronic Commerce
Event-based social networks: linking the online and offline social worlds
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Random hyperbolic graphs: degree sequence and clustering
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Extracting hierarchies with overlapping structure from network data
Proceedings of the Winter Simulation Conference
Cascade-based community detection
Proceedings of the sixth ACM international conference on Web search and data mining
Arrival and departure dynamics in social networks
Proceedings of the sixth ACM international conference on Web search and data mining
Overlapping community detection at scale: a nonnegative matrix factorization approach
Proceedings of the sixth ACM international conference on Web search and data mining
Modeling affiliations in networks
Proceedings of the Winter Simulation Conference
Potential networks, contagious communities, and understanding social network structure
Proceedings of the 22nd international conference on World Wide Web
Characterising and modelling social networks with overlapping communities
International Journal of Web Based Communities
Signals from the crowd: uncovering social relationships through smartphone probes
Proceedings of the 2013 conference on Internet measurement conference
To stay or not to stay: modeling engagement dynamics in social graphs
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Estimating the relative utility of networks for predicting user activities
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
On the precision of social and information networks
Proceedings of the first ACM conference on Online social networks
Detecting cohesive and 2-mode communities indirected and undirected networks
Proceedings of the 7th ACM international conference on Web search and data mining
Hi-index | 0.00 |
In the last decade, structural properties of several naturally arising networks (the Internet, social networks, the web graph, etc.) have been studied intensively with a view to understanding their evolution. In recent empirical work, Leskovec, Kleinberg, and Faloutsos identify two new and surprising properties of the evolution of many real-world networks: densification (the ratio of edges to vertices grows over time), and shrinking diameter (the diameter reduces over time to a constant). These properties run counter to conventional wisdom, and are certainly inconsistent with graph models prior to their work. In this paper, we present 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. Our model is based on ideas studied empirically in the social sciences, primarily on the groundbreaking work of Breiger (1973) on bipartite models of social networks that capture the affiliation of agents to societies. We also present algorithms that harness the structural consequences of our model. Specifically, we show how to overcome the bottleneck of densification in computing shortest paths between vertices by producing sparse subgraphs that preserve or approximate shortest distances to all or a distinguished subset of vertices. This is a rare example of an algorithmic benefit derived from a realistic graph model. Finally, our work also presents a modular approach to connecting random graph paradigms (preferential attachment, edge-copying, etc.) to structural consequences (heavy-tailed degree distributions, shrinking diameter, etc.).