SIAM Journal on Applied Mathematics
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
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
Spatial gossip and resource location protocols
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
A proof of alon's second eigenvalue conjecture
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The Diameter of a Scale-Free Random Graph
Combinatorica
Simple efficient load balancing algorithms for peer-to-peer systems
Proceedings of the sixteenth annual ACM symposium on Parallelism in algorithms and architectures
Modeling epidemic spreading in mobile environments
Proceedings of the 4th ACM workshop on Wireless security
Random Walk for Self-Stabilizing Group Communication in Ad Hoc Networks
IEEE Transactions on Mobile Computing
A preliminary investigation of worm infections in a bluetooth environment
Proceedings of the 4th ACM workshop on Recurring malcode
Bluetooth worm propagation: mobility pattern matters!
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Discrete Applied Mathematics
Impact of Human Mobility on Opportunistic Forwarding Algorithms
IEEE Transactions on Mobile Computing
Network Control and Optimization
A random walk model for infection on graphs
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Epidemics and Rumours in Complex Networks
Epidemics and Rumours in Complex Networks
Multiple Random Walks in Random Regular Graphs
SIAM Journal on Discrete Mathematics
Random walks in distributed computing: a survey
IICS'04 Proceedings of the 4th international conference on Innovative Internet Community Systems
Efficient generation of networks with given expected degrees
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
Viral processes by random walks on random regular graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Coalescing-branching random walks on graphs
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end, we propose a simple model of infection that enables to study the coincidence time of two random walkers on an arbitrary graph. By studying the coincidence time of a susceptible and an infected individual both moving in the graph we obtain estimates of the infection probability. The main result of this paper is to pinpoint the impact of the network topology on the infection probability. More precisely, we prove that for homogeneous graphs including regular graphs and the classical Erd驴s---Rényi model, the coincidence time is inversely proportional to the number of nodes in the graph. We then study the model on power-law graphs, that exhibit heterogeneous connectivity patterns, and show the existence of a phase transition for the coincidence time depending on the parameter of the power-law of the degree distribution. We finally undertake a preliminary analysis for the case with k random walkers and provide upper bounds on the convergence time for both the complete graph and regular graphs.