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Abstract: In the context of graph clustering, we consider the problem of simultaneously estimating both the partition of the graph nodes and the parameters of an underlying mixture of affiliation networks. In numerous applications the rapid increase of data size over time makes classical clustering algorithms too slow because of the high computational cost. In such situations online clustering algorithms are an efficient alternative to classical batch algorithms. We present an original online algorithm for graph clustering based on a Erdős–Rényi graph mixture. The relevance of the algorithm is illustrated, using both simulated and real data sets. The real data set is a network extracted from the French political blogosphere and presents an interesting community organization. [Copyright &y& Elsevier]

• Statistical analyses for variety mixtures have made little progress in recent years. • Novel models are proposed to study mixing ability in incomplete designs. • The models account for inter and intra-genotypic interactions within mixtures. • The framework handles mixtures with any order and proportions of components. • This framework was shown to be relevant on wheat mixture trial analysis. There has been recently a renewed interest for variety mixtures due to their potential capacity to stabilize production through buffering abiotic and biotic stresses. Part of this results from complementarity and/or compensation between varieties which can be assessed under mixed stands only. Mixing ability of varieties can be partitioned into General and Specific Mixing Abilities (GMA and SMA) that have been estimated so far through the evaluation of binary mixtures in complete diallel designs. However, the number of mixtures increases exponentially with the number of studied varieties, and the only feasible devices are incomplete designs. Despite the long history of statistical analysis of variety mixtures, such incomplete design analysis has rarely been addressed so far. To fill the gap, we proposed a generalized statistical framework to assess mixing abilities based on mixed models and BLUP method, with an original modeling of plant-plant interactions. The approach has been applied to a panel of 25 winter wheat genotypes observed in two contrasted experimental designs: (i) an incomplete diallel of 75 binary mixtures, and (ii) a trial including higher order mixtures (four and eight components). The use of mixing ability models improved prediction accuracy (of modeled values for observed traits) in comparison to predictions from the mean of the pure stand components, especially in the first experiment. Genetic variability was detected for the GMA of yield and its components, whereas variability for SMA was lower. GMA predictions based on the diallel trial were highly correlated with the GMA of the second trial providing accurate inter-trial predictions. A new model has been proposed to jointly account for inter and intra-genotypic interactions for specific mixing ability, thus contributing to a better understanding of mixture functioning. This framework constitutes a step forward to the screening for mixing ability, and could be further integrated into breeding programs for the development of intra- or inter-specific crop mixtures. [ABSTRACT FROM AUTHOR]