Sampling of Attributed Networks from Hierarchical Generative Models

Abstract

Network sampling is a widely used procedure in social network analysis where a random network is sampled from a generative network model (GNM). Recently proposed GNMs, allow generation of networks with more realistic structural characteristics than earlier ones. This facilitates tasks such as hypothesis testing and sensitivity analysis. However, sampling of networks with correlated vertex attributes remains a challenging problem. While the recent work of [16] has provided a promising approach for attributed-network sampling, the approach was developed for use with relatively simple GNMs and does not work well with more complex hierarchical GNMs (which can model the range of characteristics and variation observed in real world networks more accurately). In contrast to simple GNMs where the probability mass is spread throughout the space of edges more evenly, hierarchical GNMs concentrate the mass to smaller regions of the space to reflect dependencies among edges in the network-this produces more realistic network characteristics, but also makes it more difficult to identify candidate networks from the sampling space. In this paper, we propose a novel sampling method, CSAG, to sample from hierarchical GNMs and generate networks with correlated attributes. CSAG constrains every step of the sampling process to consider the structure of the GNM-in order to bias the search to regions of the space with higher likelihood. We implemented CSAG using mixed Kronecker Product Graph Models and evaluated our approach on three real-world datasets. The results show that CSAG jointly models the correlation and structure of the networks better than the state of the art. Specifically, CSAG maintains the variability of the underlying GNM while providing a ≥ 5X reduction in attribute correlation error.

Structural Diversity and Homophily

“…ese observations indicate that although the random graph models studied may satisfy a series of network properties, the common neighborhood signature is a new network property that is not adequately captured by these models. To this end, our results have important implications for random graph model design, suggesting that in addition to ing traditional network properties [21,22,34] such as degree distribution, clustering coe cient, associativity, diameter, etc., random generation models that leverage CNS may lead to graphs that are more representative of real-world networks.…”

Measuring directed triadic closure with closure coefficients

“…A fundamental property of networks across domains is the increased probability of edges existing between nodes that share a common neighbor, a phenomenon known as triadic closure (Simmel, 1908;Rapoport, 1953;Watts & Strogatz, 1998). This concept underpins various ideas in the study of networks-especially in undirected network models with symmetric relationshipsincluding the development of generative models (Leskovec et al, 2005;Jackson & Rogers, 2007;Seshadhri et al, 2012;Robles et al, 2016), community detection methods (Fortunato, 2010;Gleich & Seshadhri, 2012), and feature extraction for network-based machine learning tasks (Henderson et al, 2012;LaFond et al, 2014).…”

The Local Closure Coefficient

“…WSDM '19, February 11-15, 2019, Melbourne, VIC, Australia collaborate in the future [20]; and in citation networks, two references appearing in the same publication are more likely to cite each other [51]. The clustering of edges underlies a number of areas of network analysis, including community detection algorithms [10,12,43], feature generation in machine learning tasks on networks [17,23], and the development of generative models for networks [26,41,44]. The clustering coefficient is the standard metric for quantifying the extent to which edges of a network cluster.…”