The bipartite map equation is a tool for community detection in bipartite networks. It is an adaption of the map equation and uses the insight that random walks in bipartite networks have to alternate between the two different node types. A tuning parameter controls to what degree the bipartite network structure is used when searching for communities. Applied to real-world networks, for example authorship networks where authors are connected to articles, or social networks where researchers are connected to conferences, the bipartite map equation is capable of finding communities at different scales, depending on the chosen parametrisation.
Entropy is a concept used in information theory, thermodynamics, and statistics in general; it measures the predictability (or chaos) of a system. One application of entropy is to design efficient encodings to describe the behaviour of stochastic processes. But what does an entropy level of, say, 2.45 mean? Here, we will develop an intuition to understand entropy by looking at the definintion and behaviour of Shannon entropy.
The map equation provides a way to measure how well a clustering of the nodes in a graph captures the structure of that same graph. It takes into account the "connectedness" within and between clusters for that. In this blog post, we will cover the required background to undertand the map equation and give an implementation of the map equation in Haskell.
The first post on this blog. And it's not about monads.