Parallel Modeling of Dynamical Processes on Complex Networks

The use of High-Performance Computing methods and technologies can ultimately facilitate the investigation of dynamical processes in very large (in order of billion vertexes) networks. In particular, the generation of a large network with given properties, as well as the modeling of interactions between vertices, can be done in parallel.

We know how to generate networks with billions of nodes while simultaneously modeling the spreading of a process on a created network. As a network generative model, we use Poisson stochastic Kronecker graphs, which enable the creation of a network with a required degree distribution using the initiator matrix. Modeling the dynamic of SIRS1-like processes is performed for a given part of initially activated vertices and a probability of activation of neighbors per iteration. Message passing between the different parts of a network is done at the end of iteration using the explicit Master processes to route messages. To increase the efficiency of resource usage, a load balancing algorithm was developed taking account of the structure of the initiator matrix.

В An illustrative example is modeling the spreading of a process on a network for an initiator matrix estimated by the Barabasi-Albert network and a single Master process for message routing.

1SIRS –  a general epidemic model which describes a lifecycle of an individual during spreading of infectious disease as a transition between the states “susceptible’’ – “infected’’ – “removed (recovered) ’’ – “susceptible’’.


  • Иванов С.В., Колыхматов И.И., Бухановский А.В.

    Параллельные алгоритмы моделирования комплексных сетей // Изв. вузов. Приборостроение. — 2008. — № 51(10) — С 5-12.


  • The Russian Science Foundation #14–21–00137, 15.08.2014