Usage

This documentation will suppose that you are aware of the basics of Python and the different packages used in this project, such as [NetworkX](https://networkx.org/) or [Numpy](https://numpy.org/). If you are not, you can find a lot of tutorials on the Internet, or even on the official websites of the packages.

The commands in this file are written for Linux systems. If you are using Windows, replace python3 by py. Also, if you are using a virtual environment, you may need to replace python3 by python.

The package Network Analysis is composed of different modules, each one containing different functions. The main modules are:

• network.statistics for the computation of different statistics on graphs;

• network.ergm which contains multiple submodules for analyzing exponential random graph models.

Installation

If Python 3 is not installed on your computer, you can download it from the [official website](https://www.python.org/downloads/), or use your package manager if you are using Linux. The package Network Analysis can be installed from PyPI using the following command:

python3 -m pip install network-analysis

To force to install a specific version of the package, you can use the following command:

python3 -m pip install network-analysis==0.1.0

for the version 0.1.0 for example.

Statistics

To use the package, you first need to import the specific modules you want to use. For example, if you want to compute the geometrically weighted degree of a graph, you can use the following command:

from network-analysis import statistics as stat

# Create a graph
G = nx.Graph()
G.add_edges_from([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)])

# Compute the geometrically weighted degree
stat.gwd(G)

You can also create a function that computes a list of sufficient statistics relative to your application. Let us say we want the sufficient statistics function for a two-star model, which is the number of edges, and the number of paths of length 2. We can create the following function:

ss = stat.StatsComp([ # For Statistics Computer
    stat.NEdges(),
    stat.KStars(2),
])

and then simply use it on a graph:

ss(G)

Note: For each statistics function, such as gwd or mutuals, that network-analysis.statistics contains, it exists a class that does the same thing, but that can be used in a StatsComp object. It allows you to specify once and for all some parameters, such as the number of stars for KStars, and then use it on any graph.

Exponential Random Graph Models

The package Network Analysis also contains a lot of tools for exponential random graph models. For example, if you want to simulate a random graph from a two-star model, you can use the following command:

from network-analysis import ergm as ergm
import numpy as np

# Create a statistics computer
ss = ergm.StatsComp([
    ergm.NEdges(),
    ergm.KStars(2),
])
# Create a parameter
theta = np.array([-0.5, 1])

ergm.simulate(100, theta, ss)

The function simulate has multiple parameters to collect various information on Markov chain used to simulate the random graph. You can find more information on the documentation of the function.

Suppose now that you observed a graph G and you want to compute the maximum likelihood estimator of the parameter of a two-star model with the statistics compute ss. You can use the following command:

ergm.ml(G, ss)

The submodule ergm.likelihood contains multiple functions such as ml that can be used to compute the maximum likelihood estimator, mpl that computes the maximum pseudolikelihood, or apl for getting the adjusted pseudolikelihood function. For more information, you can refer to the documentation.