Network histograms and universality of blockmodel approximation

Sofia C. Olhede and Patrick J. Wolfe

PNAS 111(41):14722-14727

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

Stochastic block model

From Guimerà and Sales-Pardo (2009) PNAS 106(52):22073-78

Stochastic block model

From Aaron Clauset lectures, Santa Fe Institute 2013

Real data

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.

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

Political weblogs

Political weblogs

School friendship data

School friendship data