Exact Recovery for a Family of Community-Detection Generative Models

Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models called planted Random Energy Model (REM), inspired by Derrida's REM. For this model we provide the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold. As an application, we further consider the 2 non-equally sized community Weighted Stochastic Block Model (2-WSBM) on $h$-uniform hypergraphs, that is equivalent to the P-REM on both sides of the spectrum, for high and low edge cardinality $h$. We provide upper and lower bounds for the exact recoverability for any $h$, mapping these problems to the aforementioned P-REM. To the best of our knowledge these are the first consistency results for the 2-WSBM on graphs and on hypergraphs with non-equally sized community

Modeling heterogeneity in random graphs through latent space models: a selective review

We present a selective review on probabilistic modeling of heterogeneity in random graphs. We focus on latent space models and more particularly on stochastic block models and their extensions that have undergone major developments in the last five years

The one comparing narrative social network extraction techniques

Analysing narratives through their social networks is an expanding field in quantitative literary studies. Manually extracting a social network from any narrative can be time consuming, so automatic extraction methods of varying complexity have been developed. However, the effect of different extraction methods on the resulting networks is unknown. Here we model and compare three extraction methods for social networks in narratives: manual extraction, co-occurrence automated extraction and automated extraction using machine learning. Although the manual extraction method produces more precise results in the network analysis, it is highly time consuming. The automatic extraction methods yield comparable results for density, centrality measures and edge weights. Our results provide evidence that automatically-extracted social networks are reliable for many analyses. We also describe which aspects of analysis are not reliable with such a social network. Our findings provide a framework to analyse narratives, which help us improve our understanding of how stories are written and evolve, and how people interact with each other. Index Tenns-social networks, narratives, televisionMichelle Edwards, Jonathan Tuke, Matthew Roughan, Lewis Mitchel