1. Network histograms and universality of blockmodel approximation Sofia C. Olhede and Patrick J. Wolfe PNAS 111(41):14722-14727

2. Stochastic block model From Guimerà and Sales-Pardo (2009) PNAS 106(52):22073-78 a generative model for graphs with heterogenous degrees. often used as model for learning community structure. can predict missing edges in the network

3. Stochastic block model From Guimerà and Sales-Pardo (2009) PNAS 106(52):22073-78

4. Stochastic block model From Aaron Clauset lectures, Santa Fe Institute 2013

5. Real data

6. Key concepts A graphon is a continuous 2D probability density function for interactions between nodes. The structure of any network can be described by its number of nodes n and an appropriate graphon.

7. Describing networks using histograms Instead of learning a block model, we will look for a histogram approximation of the graphon that best fits the data. The authors provide an error metric to support a maximum likelihood estimation of the best bin width to choose. Code is provided! https://github.com/p-wolfe/network-histogram-code

8. Political weblogs

10. School friendship data