32 research outputs found
On the Spread of Viruses on the Internet
We analyze the contact process on random graphs generated according to the preferential attachment scheme as a model for the spread of viruses in the Internet. We show that any virus with a positive rate of spread from a node to its neighbors has a non-vanishing chance of becoming epidemic. Quantitatively, we discover an interesting dichotomy: for it virus with effective spread rate λ, if the infection starts at a typical vertex, then it develops into an epidemic with probability λ^Θ ((log (1/ λ)/log log (1/ λ))), but on average the epidemic probability is λ^(Θ (1))
Preferential attachment hypergraph with high modularity
Numerous works have been proposed to generate random graphs preserving the
same properties as real-life large scale networks. However, many real networks
are better represented by hypergraphs. Few models for generating random
hypergraphs exist and no general model allows to both preserve a power-law
degree distribution and a high modularity indicating the presence of
communities. We present a dynamic preferential attachment hypergraph model
which features partition into communities. We prove that its degree
distribution follows a power-law and we give theoretical lower bounds for its
modularity. We compare its characteristics with a real-life co-authorship
network and show that our model achieves good performances. We believe that our
hypergraph model will be an interesting tool that may be used in many research
domains in order to reflect better real-life phenomena