485 research outputs found
Model-based clustering for populations of networks
Until recently obtaining data on populations of networks was typically rare.
However, with the advancement of automatic monitoring devices and the growing
social and scientific interest in networks, such data has become more widely
available. From sociological experiments involving cognitive social structures
to fMRI scans revealing large-scale brain networks of groups of patients, there
is a growing awareness that we urgently need tools to analyse populations of
networks and particularly to model the variation between networks due to
covariates. We propose a model-based clustering method based on mixtures of
generalized linear (mixed) models that can be employed to describe the joint
distribution of a populations of networks in a parsimonious manner and to
identify subpopulations of networks that share certain topological properties
of interest (degree distribution, community structure, effect of covariates on
the presence of an edge, etc.). Maximum likelihood estimation for the proposed
model can be efficiently carried out with an implementation of the EM
algorithm. We assess the performance of this method on simulated data and
conclude with an example application on advice networks in a small business.Comment: The final (published) version of the article can be downloaded for
free (Open Access) from the editor's website (click on the DOI link below
Enhanced detectability of community structure in multilayer networks through layer aggregation
Many systems are naturally represented by a multilayer network in which edges
exist in multiple layers that encode different, but potentially related, types
of interactions, and it is important to understand limitations on the
detectability of community structure in these networks. Using random matrix
theory, we analyze detectability limitations for multilayer (specifically,
multiplex) stochastic block models (SBMs) in which L layers are derived from a
common SBM. We study the effect of layer aggregation on detectability for
several aggregation methods, including summation of the layers' adjacency
matrices for which we show the detectability limit vanishes as O(L^{-1/2}) with
increasing number of layers, L. Importantly, we find a similar scaling behavior
when the summation is thresholded at an optimal value, providing insight into
the common - but not well understood - practice of thresholding
pairwise-interaction data to obtain sparse network representations.Comment: 7 pages, 4 figure
Random graph models for dynamic networks
We propose generalizations of a number of standard network models, including
the classic random graph, the configuration model, and the stochastic block
model, to the case of time-varying networks. We assume that the presence and
absence of edges are governed by continuous-time Markov processes with rate
parameters that can depend on properties of the nodes. In addition to computing
equilibrium properties of these models, we demonstrate their use in data
analysis and statistical inference, giving efficient algorithms for fitting
them to observed network data. This allows us, for instance, to estimate the
time constants of network evolution or infer community structure from temporal
network data using cues embedded both in the probabilities over time that node
pairs are connected by edges and in the characteristic dynamics of edge
appearance and disappearance. We illustrate our methods with a selection of
applications, both to computer-generated test networks and real-world examples.Comment: 15 pages, four figure
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