Statistical properties of sampled networks

One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real life networks due to their differences on other important metrics like conductance. We believe this is, in part, beca...

Many real-world networks are large, complex and thus hard to understand, analyze or visualize. The data about networks is not always complete, their structure may be hidden or they change quickly over time. Therefore, understanding how incomplete system differs from complete one is crucial. In this paper, we study the changes in networks under simplification (i.e., reduction in size). We simplify 30 real-world networks with six simplification methods and analyze the similarit...

Previous studies on the invulnerability of scale-free networks under edge attacks supported the conclusion that scale-free networks would be fragile under selective attacks. However, these studies are based on qualitative methods with obscure definitions on the robustness. This paper therefore employs a quantitative method to analyze the invulnerability of the scale-free networks, and uses four scale-free networks as the experimental group and four random networks as the cont...

Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is still underway. We propose bootstrap subsampling methods for finding empirical distribution of count features or ``moments'' (Bickel, Chen and Levina [Ann. Statist. 39 (2011) 2280-2301]) and smooth functions of these features for the networks...

We present an algorithm for generating random networks with arbitrary degree distribution and Clustering (frequency of triadic closure). We use this algorithm to generate networks with exponential, power law, and poisson degree distributions with variable levels of clustering. Such networks may be used as models of social networks and as a testable null hypothesis about network structure. Finally, we explore the effects of clustering on the point of the phase transition where...

A great deal of effort has been spent measuring topological features of the Internet. However, it was recently argued that sampling based on taking paths or traceroutes through the network from a small number of sources introduces a fundamental bias in the observed degree distribution. We examine this bias analytically and experimentally. For Erdos-Renyi random graphs with mean degree c, we show analytically that traceroute sampling gives an observed degree distribution P(k) ...

We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights are given by the edge betweenness centralities. We find that a scale-free tree and shortcuts organize a complex network. The spanning tree shows robust betweenness centrality distribution that was observed in scale-free tree models. It turns...

We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability distribution of any network node-based property, and of the network size, after only a small fraction of network nodes has been explored. The Bayesian nature of our approach provides rigorous estimates of all parameter uncertainties. We demonstrate...

With network data becoming ubiquitous in many applications, many models and algorithms for network analysis have been proposed. Yet methods for providing uncertainty estimates in addition to point estimates of network parameters are much less common. While bootstrap and other resampling procedures have been an effective general tool for estimating uncertainty from i.i.d. samples, adapting them to networks is highly nontrivial. In this work, we study three different network re...

This article aims at summarizing the existing methods for sampling social networking services and proposing a faster confidence interval for related sampling methods. It also includes comparisons of common network sampling techniques.