159 research outputs found
Discrete Temporal Models of Social Networks
We propose a family of statistical models for social network evolution over
time, which represents an extension of Exponential Random Graph Models (ERGMs).
Many of the methods for ERGMs are readily adapted for these models, including
maximum likelihood estimation algorithms. We discuss models of this type and
their properties, and give examples, as well as a demonstration of their use
for hypothesis testing and classification. We believe our temporal ERG models
represent a useful new framework for modeling time-evolving social networks,
and rewiring networks from other domains such as gene regulation circuitry, and
communication networks
A Separable Model for Dynamic Networks
Models of dynamic networks --- networks that evolve over time --- have
manifold applications. We develop a discrete-time generative model for social
network evolution that inherits the richness and flexibility of the class of
exponential-family random graph models. The model --- a Separable Temporal ERGM
(STERGM) --- facilitates separable modeling of the tie duration distributions
and the structural dynamics of tie formation. We develop likelihood-based
inference for the model, and provide computational algorithms for maximum
likelihood estimation. We illustrate the interpretability of the model in
analyzing a longitudinal network of friendship ties within a school.Comment: 28 pages (including a 4-page appendix); a substantial rewrite, with
many corrections, changes in terminology, and a different analysis for the
exampl
Disease spread over randomly switched large-scale networks
In this paper we study disease spread over a randomly switched network, which
is modeled by a stochastic switched differential equation based on the so
called -intertwined model for disease spread over static networks. Assuming
that all the edges of the network are independently switched, we present
sufficient conditions for the convergence of infection probability to zero.
Though the stability theory for switched linear systems can naively derive a
necessary and sufficient condition for the convergence, the condition cannot be
used for large-scale networks because, for a network with agents, it
requires computing the maximum real eigenvalue of a matrix of size exponential
in . On the other hand, our conditions that are based also on the spectral
theory of random matrices can be checked by computing the maximum real
eigenvalue of a matrix of size exactly
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