1,251 research outputs found
Estimation of subgraph density in noisy networks
While it is common practice in applied network analysis to report various
standard network summary statistics, these numbers are rarely accompanied by
uncertainty quantification. Yet any error inherent in the measurements
underlying the construction of the network, or in the network construction
procedure itself, necessarily must propagate to any summary statistics
reported. Here we study the problem of estimating the density of an arbitrary
subgraph, given a noisy version of some underlying network as data. Under a
simple model of network error, we show that consistent estimation of such
densities is impossible when the rates of error are unknown and only a single
network is observed. Accordingly, we develop method-of-moment estimators of
network subgraph densities and error rates for the case where a minimal number
of network replicates are available. These estimators are shown to be
asymptotically normal as the number of vertices increases to infinity. We also
provide confidence intervals for quantifying the uncertainty in these estimates
based on the asymptotic normality. To construct the confidence intervals, a new
and non-standard bootstrap method is proposed to compute asymptotic variances,
which is infeasible otherwise. We illustrate the proposed methods in the
context of gene coexpression networks
Bayesian Inference of Online Social Network Statistics via Lightweight Random Walk Crawls
Online social networks (OSN) contain extensive amount of information about
the underlying society that is yet to be explored. One of the most feasible
technique to fetch information from OSN, crawling through Application
Programming Interface (API) requests, poses serious concerns over the the
guarantees of the estimates. In this work, we focus on making reliable
statistical inference with limited API crawls. Based on regenerative properties
of the random walks, we propose an unbiased estimator for the aggregated sum of
functions over edges and proved the connection between variance of the
estimator and spectral gap. In order to facilitate Bayesian inference on the
true value of the estimator, we derive the approximate posterior distribution
of the estimate. Later the proposed ideas are validated with numerical
experiments on inference problems in real-world networks
Subgraph covers -- An information theoretic approach to motif analysis in networks
Many real world networks contain a statistically surprising number of certain
subgraphs, called network motifs. In the prevalent approach to motif analysis,
network motifs are detected by comparing subgraph frequencies in the original
network with a statistical null model. In this paper we propose an alternative
approach to motif analysis where network motifs are defined to be connectivity
patterns that occur in a subgraph cover that represents the network using
minimal total information. A subgraph cover is defined to be a set of subgraphs
such that every edge of the graph is contained in at least one of the subgraphs
in the cover. Some recently introduced random graph models that can incorporate
significant densities of motifs have natural formulations in terms of subgraph
covers and the presented approach can be used to match networks with such
models. To prove the practical value of our approach we also present a
heuristic for the resulting NP-hard optimization problem and give results for
several real world networks.Comment: 10 pages, 7 tables, 1 Figur
Growing Graphs with Hyperedge Replacement Graph Grammars
Discovering the underlying structures present in large real world graphs is a
fundamental scientific problem. In this paper we show that a graph's clique
tree can be used to extract a hyperedge replacement grammar. If we store an
ordering from the extraction process, the extracted graph grammar is guaranteed
to generate an isomorphic copy of the original graph. Or, a stochastic
application of the graph grammar rules can be used to quickly create random
graphs. In experiments on large real world networks, we show that random
graphs, generated from extracted graph grammars, exhibit a wide range of
properties that are very similar to the original graphs. In addition to graph
properties like degree or eigenvector centrality, what a graph "looks like"
ultimately depends on small details in local graph substructures that are
difficult to define at a global level. We show that our generative graph model
is able to preserve these local substructures when generating new graphs and
performs well on new and difficult tests of model robustness.Comment: 18 pages, 19 figures, accepted to CIKM 2016 in Indianapolis, I
- …