Earlier this year I gave at the talk at the March 4th, 2011 meeting of SCONE (Scottish Networking Event), on “Distributed k-shell graph decomposition”. The talk is on the k-core or k-shell of a graph, given in papers such as Seidman’s “Network Structure and Minimum Degree”, and it presents a new, efficient, distributed, algorithm for computing the maximal k-core membership of each node.
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Paul Jakma's Blog 
Paul Jakma said
Short paper published by CoNext 2012, with an overview of proof, and describing an extension to allow the algorithm to work on dynamic graphs.