The inference of network topologies from relational data is an important problem in data analysis. Exemplary applications include the reconstruction of social ties from data on human interactions, the inference of gene co-expression networks from DNA microarray data, or the learning of semantic relationships based on co-occurrences of words in documents. Solving these problems requires techniques to infer significant links in noisy relational data. In this short paper, we propose a new statistical modeling framework to address this challenge. It builds on generalized hypergeometric ensembles, a class of generative stochastic models that give rise to analytically tractable probability spaces of directed, multi-edge graphs. We show how this framework can be used to assess the significance of links in noisy relational data. We illustrate our method in two data sets capturing spatio-temporal proximity relations between actors in a social system. The results show that our analytical framework provides a new approach to infer significant links from relational data, with interesting perspectives for the mining of data on social systems.

Statistical ensembles of networks, i.e., probability spaces of all networks that are consistent with given aggregate statistics, have become instrumental in the analysis of complex networks. Their numerical and analytical study provides the foundation for the inference of topological patterns, the definition of network-analytic measures, as well as for model selection and statistical hypothesis testing. Contributing to the foundation of these data analysis techniques, in this Letter we introduce generalized hypergeometric ensembles, a broad class of analytically tractable statistical ensembles of finite, directed and weighted networks. This framework can be interpreted as a generalization of the classical configuration model, which is commonly used to randomly generate networks with a given degree sequence or distribution. Our generalization rests on the introduction of dyadic link propensities, which capture the degree-corrected tendencies of pairs of nodes to form edges between each other. Studying empirical and synthetic data, we show that our approach provides broad perspectives for model selection and statistical hypothesis testing in data on complex networks.

Multi-edge networks capture repeated interactions between individuals. In social networks, such edges often form closed triangles, or triads. Standard approaches to measure this triadic closure, however, fail for multi-edge networks, because they do not consider that triads can be formed by edges of different multiplicity. We propose a novel measure of triadic closure for multi-edge networks of social interactions based on a shared partner statistic. We demonstrate that our operalization is able to detect meaningful closure in synthetic and empirical multi-edge networks, where common approaches fail. This is a cornerstone in driving inferential network analyses from the analysis of binary networks towards the analyses of multi-edge and weighted networks, which offer a more realistic representation of social interactions and relations.

The unsupervised detection of anomalies in time series data has important applications, e.g., in user behavioural modelling, fraud detection, and cybersecurity. Anomaly detection has been extensively studied in categorical sequences. But we often have access to time series data that contain paths in networks. Examples include transaction sequences in financial networks, click streams of users in networks of cross-referenced documents, or travel itineraries in transportation networks. To reliably detect anomalies we must account for the fact that such data contain a large number of independent observations of short paths constrained by a graph topology. Moreover, the heterogeneity of real systems rules out frequencybased anomaly detection techniques, which do not account for highly skewed edge and degree statistics. To address this problem we introduce HYPA, a novel framework for the unsupervised detection of anomalies in large corpora of variable-length temporal paths in a graph. HYPA provides an efficient analytical method to detect paths with anomalous frequencies that result from nodes being traversed in unexpected chronological order.

Established Open Source Software (OSS) projects can grow in size if new developers join, but also the number of OSS projects can grow if developers choose to found new projects. We discuss to what extent an established model for firm growth can be applied to the dynamics of OSS projects. Our analysis is based on a large-scale data set from SourceForge (SF) consisting of monthly data for 10 years, for up to 360 000 OSS projects and up to 340 000 developers. Over this time period, we find an exponential growth both in the number of projects and developers, with a remarkable increase of single-developer projects after 2009. We analyze the monthly entry and exit rates for both projects and developers, the growth rate of established projects and the monthly project size distribution. To derive a prediction for the latter, we use modeling assumptions of how newly entering developers choose to either found a new project or to join existing ones. Our model applies only to collaborative projects that are deemed to grow in size by attracting new developers. We verify, by a thorough statistical analysis, that the Yule-Simon distribution is a valid candidate for the size distribution of collaborative projects except for certain time periods where the modeling assumptions no longer hold. We detect and empirically test the reason for this limitation, i.e., the fact that an increasing number of established developers found additional new projects after 2009.