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
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
Degree Distribution of Competition-Induced Preferential Attachment Graphs
Combinatorics, Probability and Computing
On certain connectivity properties of the internet topology
Journal of Computer and System Sciences - Special issue on FOCS 2003
Degree distribution of the FKP network model
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
The web as a graph: measurements, models, and methods
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Social networks spread rumors in sublogarithmic time
Proceedings of the forty-third annual ACM symposium on Theory of computing
Why rumors spread so quickly in social networks
Communications of the ACM
Critical Infrastructure Protection
Experimental analysis of rumor spreading in social networks
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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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 $x_t$ and $m$ random edges incident with $x_t$, where $m$ is constant. The neighbours of $x_t$ 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 $\delta n$, where $\delta$ is a constant. We show that if $\delta$ is sufficiently small and $m$ is sufficiently large then with high probability at time $n$ the generated graph has a component of size at least $n/30$.