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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Edge-exchangeable graphs, sparsity, and power laws

## Edge-exchangeable graphs, sparsity, and power lawsAdd to your list(s) Download to your calendar using vCal - Diana Cai (University of Chicago)
- Wednesday 27 July 2016, 12:00-12:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. SNAW05 - Bayesian methods for networks Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or empty with probability one, whereas many real-world graphs are sparse. We present an alternative notion of exchangeability for random graphs, which we call edge exchangeability, in which the distribution of a graph sequence is invariant to the order of the edges. We characterize the class of edge exchangeable models with a paintbox construction, and we demonstrate that edge-exchangeable models, unlike models that are traditionally vertex exchangeable, can exhibit sparsity and power laws. To do so, we outline a general framework for graph generative models; by contrast to the pioneering work of Caron and Fox (2014), models within our framework are stationary across steps of the graph sequence. In particular, our model grows the graph by instantiating more latent atoms of a single random measure as the dataset size increases, rather than adding new atoms to the measure. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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