353 research outputs found
Exchangeable Random Networks
We introduce and study a class of exchangeable random graph ensembles. They
can be used as statistical null models for empirical networks, and as a tool
for theoretical investigations. We provide general theorems that carachterize
the degree distribution of the ensemble graphs, together with some features
that are important for applications, such as subgraph distributions and kernel
of the adjacency matrix. These results are used to compare to other models of
simple and complex networks. A particular case of directed networks with
power-law out--degree is studied in more detail, as an example of the
flexibility of the model in applications.Comment: to appear on "Internet Mathematics
Graph limits and exchangeable random graphs
We develop a clear connection between deFinetti's theorem for exchangeable
arrays (work of Aldous--Hoover--Kallenberg) and the emerging area of graph
limits (work of Lovasz and many coauthors). Along the way, we translate the
graph theory into more classical probability.Comment: 26 page
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