Isomorphism and embedding problems for infinite limits of scale-free graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Adversarial deletion in a scale free random graph process
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the spread of viruses on the internet
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graphs over time: densification laws, shrinking diameters and possible explanations
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
The Small Giant Component in Scale-Free Random Graphs
Combinatorics, Probability and Computing
Generalizing PageRank: damping functions for link-based ranking algorithms
SIGIR '06 Proceedings of the 29th annual international ACM SIGIR conference on Research and development in information retrieval
Random walk based node sampling in self-organizing networks
ACM SIGOPS Operating Systems Review
Distribution of Vertex Degree in Web-Graphs
Combinatorics, Probability and Computing
Thresholds for virus spread on networks
valuetools '06 Proceedings of the 1st international conference on Performance evaluation methodolgies and tools
Graph evolution: Densification and shrinking diameters
ACM Transactions on Knowledge Discovery from Data (TKDD)
The cover time of the preferential attachment graph
Journal of Combinatorial Theory Series B
Adversarial Deletion in a Scale-Free Random Graph Process
Combinatorics, Probability and Computing
The degree distribution of the generalized duplication model
Theoretical Computer Science
Degree distribution of the FKP network model
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First to market is not everything: an analysis of preferential attachment with fitness
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The phase transition in inhomogeneous random graphs
Random Structures & Algorithms
End-to-end loss probabilities in different internet-like networks with a given average hop count
ICCOM'07 Proceedings of the 11th Conference on 11th WSEAS International Conference on Communications - Volume 11
Gossiping (via mobile?) in social networks
Proceedings of the fifth international workshop on Foundations of mobile computing
Proceedings of the forty-first annual ACM symposium on Theory of computing
Modeling and Designing Real---World Networks
Algorithmics of Large and Complex Networks
Rumor Spreading in Social Networks
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
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
A random walk model for infection on graphs
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Performance evaluation of immunity-based diagnosis on complex networks
KES'07/WIRN'07 Proceedings of the 11th international conference, KES 2007 and XVII Italian workshop on neural networks conference on Knowledge-based intelligent information and engineering systems: Part III
A geometric preferential attachment model of networks II
WAW'07 Proceedings of the 5th international conference on Algorithms and models for the web-graph
Non-searchability of random power-law graphs
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Role model based mechanism for norm emergence in artificial agent societies
COIN'07 Proceedings of the 2007 international conference on Coordination, organizations, institutions, and norms in agent systems III
On the impact of the migration topology on the Island Model
Parallel Computing
The diameter of sparse random graphs
Combinatorics, Probability and Computing
A random walk model for infection on graphs: spread of epidemics & rumours with mobile agents
Discrete Event Dynamic Systems
Random Walks with Look-Ahead in Scale-Free Random Graphs
SIAM Journal on Discrete Mathematics
Rumor spreading in social networks
Theoretical Computer Science
The clustering coefficient of a scale-free random graph
Discrete Applied Mathematics
The influence of network topological models on the prediction of end-to-end loss probabilities
MIV'05 Proceedings of the 5th WSEAS international conference on Multimedia, internet & video technologies
Social networks spread rumors in sublogarithmic time
Proceedings of the forty-third annual ACM symposium on Theory of computing
Numerical optimization of generative network parameters
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
Construction of scale-free networks with partial information
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
A survey of models of the web graph
CAAN'04 Proceedings of the First international conference on Combinatorial and Algorithmic Aspects of Networking
Forest search: a paradigm for faster exploration of scale-free networks
ISPA'06 Proceedings of the 4th international conference on Parallel and Distributed Processing and Applications
Why rumors spread so quickly in social networks
Communications of the ACM
A fast algorithm to find all high degree vertices in power law graphs
Proceedings of the 21st international conference companion on World Wide Web
Critical Infrastructure Protection
Some typical properties of the spatial preferred attachment model
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
On certain properties of random apollonian networks
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
Asynchronous rumor spreading in preferential attachment graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Impact of dynamic growing on the internet degree distribution
ISPA'07 Proceedings of the 2007 international conference on Frontiers of High Performance Computing and Networking
Proceedings of the 21st ACM international conference on Information and knowledge management
The power of local information in social networks
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
Experimental analysis of rumor spreading in social networks
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
Cooperative stalking of transient nomadic resources on overlay networks
Future Generation Computer Systems
Centralized and distributed protocols for tracker-based dynamic swarm management
IEEE/ACM Transactions on Networking (TON)
Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles
ACM SIGOPS 24th Symposium on Operating Systems Principles
X-Stream: edge-centric graph processing using streaming partitions
Proceedings of the Twenty-Fourth ACM Symposium on Operating Systems Principles
| Hi-index | 0.02 |
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 probability proportional to its degree. This process was introduced by Barabási and Albert [3], as a simple model of the growth of real-world graphs such as the world-wide web. Computer experiments presented by Barabási, Albert and Jeong [1,5] and heuristic arguments given by Newman, Strogatz and Watts [23] suggest that after n steps the resulting graph should have diameter approximately logn. We show that while this holds for m=1, for m≥2 the diameter is asymptotically log n/log logn.