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Exponential Random Graph Models in Python

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# pyERGM - A Python implementation for ERGM's

An exponential random graphs model (**ERGM**) is a statistical model that describes a distribution of random graphs. This package provides a simple and easy way to fit and sample from ERGMs.

An ERGM defines a random variable $\mathbf{Y}$, which is simply a random graph on $n$ nodes. The probability of observing a specific graph $y\in \lbrace 0,1 \rbrace ^{n \times n}$ is given by -

$$\Pr(\mathbf{Y}=y | \theta) = \frac{\exp(\theta^Tg(y))}{\sum_{z\in\mathcal{Y}} \exp(\theta^Tg(z))}$$

where $g(y)$ is a vector of statistics that describe the graph $y$, and $\theta \in \mathbb{R}^q$ is a vector of model parameters. Each graph is represented by a binary adjacency matrix, where $y_{ij}=1$ if there is an edge between nodes $i$ and $j$ (and $y_{ji}=1$ in the undirected case).

Fitting a model for even moderately large graphs can be a computationally challenging task. pyERGM keeps this in mind and is implemented to be efficient and scalable by using `numpy` and `Numba`, as well as providing an interface for fitting models on a distributed computing environment.

[View the full documentation here](https://tomtalp.github.io/pyERGM/)

## Installation
https://pypi.org/project/pyERGM/

## Getting started
Fitting an ERGM model requires a graph and a set of statistics that describe the graph. The model is then fit by maximizing the likelihood of the observed graph under the model.

The following example demonstrates how to fit a simple ERGM model from [Sampson's monastery data](https://networkdata.ics.uci.edu/netdata/html/sampson.html).

```python
from pyERGM.ergm import ERGM
from pyERGM.metrics import *
from pyERGM.datasets import sampson_matrix

num_nodes = sampson_matrix.shape[0]
is_directed = True
metrics = [NumberOfEdgesDirected(), TotalReciprocity()]

model = ERGM(num_nodes, metrics, is_directed=is_directed)
model.fit(sampson_matrix)
```

The above example fits a model from the Sampson's monastery data using the number of edges and total reciprocity as statistics. The graph is represented as an adjacency matrix.

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