Name
Abstract | ||
|---|---|---|
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following limitation: Markovian random graphs can only replicate switching patterns with exponential inter-switching times, while in real applications these times are usually far from exponential. In this paper, we introduce a flexible and tractable extended family of processes able to replicate, with arbitrary accuracy, any distribution of inter-switching times. We then study the stability of spreading processes in this extended family. We first show that a direct analysis based on Itou0027s formula provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of edges. To overcome this limitation, we derive alternative stability conditions involving the eigenvalues of a matrix whose size grows linearly with the number of nodes. Based on our results, we also show that heuristics based on aggregated static networks approximate the epidemic threshold more accurately as the number of nodes grows, or the temporal volatility of the random graph process is reduced. Finally, we illustrate our findings via numerical simulations. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1109/TNSE.2016.2516346 | IEEE Transactions Network Science and Engineering |
Keywords | Field | DocType |
Markov processes,complex networks,eigenvalues and eigenfunctions,graph theory,matrix algebra,network theory (graphs),stability,time-varying networks,Ito formula,Markovian random graph process,aggregated static network,epidemic threshold,exponential interswitching times,interswitching time distribution,matrix eigenvalues,numerical simulation,spreading process dynamics,spreading process stability,stability conditions,switching pattern,time-varying large-scale networks,Dynamic random graphs,complex networks,epidemics,random matrix theory,stochastic processes | Discrete mathematics,Mathematical optimization,Random graph,Exponential function,Matrix (mathematics),Stochastic process,Complex network,Numerical stability,Mathematics,Random matrix,Exponential growth | Journal |
Volume | Issue | ISSN |
abs/1507.07017 | 1 | 2327-4697 |
Citations | PageRank | References |
16 | 0.80 | 16 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Masaki Ogura | 1 | 44 | 13.38 |
| Victor M. Preciado | 2 | 205 | 29.44 |