9,945 research outputs found
Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks
Stochastic simulations are one of the cornerstones of the analysis of
dynamical processes on complex networks, and are often the only accessible way
to explore their behavior. The development of fast algorithms is paramount to
allow large-scale simulations. The Gillespie algorithm can be used for fast
simulation of stochastic processes, and variants of it have been applied to
simulate dynamical processes on static networks. However, its adaptation to
temporal networks remains non-trivial. We here present a temporal Gillespie
algorithm that solves this problem. Our method is applicable to general Poisson
(constant-rate) processes on temporal networks, stochastically exact, and up to
multiple orders of magnitude faster than traditional simulation schemes based
on rejection sampling. We also show how it can be extended to simulate
non-Markovian processes. The algorithm is easily applicable in practice, and as
an illustration we detail how to simulate both Poissonian and non-Markovian
models of epidemic spreading. Namely, we provide pseudocode and its
implementation in C++ for simulating the paradigmatic
Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and
a Susceptible-Infected-Recovered model with non-constant recovery rates. For
empirical networks, the temporal Gillespie algorithm is here typically from 10
to 100 times faster than rejection sampling.Comment: Minor changes and updates to reference
How memory generates heterogeneous dynamics in temporal networks
Empirical temporal networks display strong heterogeneities in their dynamics,
which profoundly affect processes taking place on these networks, such as rumor
and epidemic spreading. Despite the recent wealth of data on temporal networks,
little work has been devoted to the understanding of how such heterogeneities
can emerge from microscopic mechanisms at the level of nodes and links. Here we
show that long-term memory effects are present in the creation and
disappearance of links in empirical networks. We thus consider a simple
generative modeling framework for temporal networks able to incorporate these
memory mechanisms. This allows us to study separately the role of each of these
mechanisms in the emergence of heterogeneous network dynamics. In particular,
we show analytically and numerically how heterogeneous distributions of contact
durations, of inter-contact durations and of numbers of contacts per link
emerge. We also study the individual effect of heterogeneities on dynamical
processes, such as the paradigmatic Susceptible-Infected epidemic spreading
model. Our results confirm in particular the crucial role of the distributions
of inter-contact durations and of the numbers of contacts per link
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