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

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Presentation on theme: "Network histograms and universality of blockmodel approximation Sofia C. Olhede and Patrick J. Wolfe PNAS 111(41):14722-14727."— Presentation transcript:

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

9

10 School friendship data

11


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