On power-law relationships of the Internet topology
Proceedings of the conference on Applications, technologies, architectures, and protocols for computer communication
Small worlds: the dynamics of networks between order and randomness
Small worlds: the dynamics of networks between order and randomness
A random graph model for massive graphs
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 '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
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
On Certain Connectivity Properties of the Internet Topology
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The Diameter of a Scale-Free Random Graph
Combinatorica
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Gossiping (via mobile?) in social networks
Proceedings of the fifth international workshop on Foundations of mobile computing
Rumor Spreading in Social Networks
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Assessing the vulnerability of replicated network services
Proceedings of the 6th International COnference
Rumor spreading in social networks
Theoretical Computer Science
Shortest-path queries for complex networks: exploiting low tree-width outside the core
Proceedings of the 15th International Conference on Extending Database Technology
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We study a dynamically evolving random graph which adds vertices and edges using preferential attachment and is "attacked by an adversary". At time t, we add a new vertex xt and m random edges incident with xt, where m is constant. The neighbors of xt are chosen with probability proportional to degree. After adding the edges, the adversary is allowed to delete vertices. The only constraint on the adversarial deletions is that the total number of vertices deleted by time n must be no larger than δn, where δ is a constant. We show that if δ is sufficiently small then with high probability at time n the generated graph has a component of size Ω(n).