dormrod/maximum_entropy

Calculates maximum entropy degree and joint degree distributions for generic networks.

Maximum Entropy Distributions

This repository contains python scripts to calculate maximum entropy node degree distributions and edge joint degree distributions.

Requirements

• Python 3.6 or higher
• Numpy
• Scipy
• Matplotlib

Node degree distribution (Lemaitre's Law)

Calculates maximum entropy node degree distributions with a specified mean and principle value (e.g. p₆).

This is achieved through the NodeME class found in node_me.py. A model is set up with a given mean and node size limits:

from node_me import NodeME

model = NodeME(k_mean=6.0, k_limits=(3,12))

The maximum entropy distribution can then be obtained given the value for a single node size (suggested to be the most common) via:

distribution = model(0.5,k=6)

Alternatively distributions can be calculated across a range of variances using:

model.scan()
model.write()

which will write the distributions and variances to node_dist.dat. These will not necessarily be evenly spaced, and so it may be preferable to use the call function in a loop.

Edge joint degree distribution

Calculates maximum entropy edge joint degree distribution with a specified mean, assortative mixing and principle value (e.g. p₆). This is achieved through the EdgeME class found in edge_me.py. A model is set up with a given mean and node size limits:

from edge_me import EdgeME

model = EdgeME(k_mean=6.0, k_limits=(3,12))

The maximum entropy joint distribution can then be obtained given the node degree distribution value for a single node size (suggested to be the most common) and the assortative mixing via:

edge_dist, node_dist, assortativity = model(0.5,-0.2,k=6)

which also provides the node distribution and assortativity.