Inference in large random graphs

Many inference problems amount to finding structure hidden in some large data set. Examples include:• community detection, ie clustering of graph nodes into groups of nodes with statistically similar properties (applications: recommender systems for online social networks; functional groups of proteins in cell chemistry)• graph alignment, ie finding a mapping of one graph's nodes to another one's that is at least approximately a graph isomorphism (applications: automatic translation; deanonymization of databases)• matrix completion, ie filling missing entries of large matrix so that the result has low rank (application: recommender systems)