# Tutorials¶

## Models¶

This tutorial presents several random graph models: the Erdos-Renyi (ER) model, degree-corrected ER model, stochastic block model (SBM), degree-corrected SBM, and random dot product graph model. These models provide a basis for studying random graphs. All models are shown fit to the same dataset.

## Simulations¶

The following tutorials demonstrate how to easily sample random graphs from graph models such as the Erdos-Renyi model, stochastic block model, and random dot product graph (RDPG).

## Clustering¶

The following tutorials explain how to cluster vertex or graph embeddings with two clustering algorithms, as well as the advantages of these to comparable implementations.

## Embedding¶

Inference on random graphs depends on low-dimensional Euclidean representation of the vertices of graphs, known as graph embeddings, typically given by spectral decompositions of adjacency or Laplacian matrices. Below are tutorials for computing graph embeddings of single graph and multiple graphs.

## Inference¶

Statistical testing on graphs requires specialized methodology in order to account for the fact that the edges and nodes of a graph are dependent on one another. Below are tutorials for robust statistical hypothesis testing on multiple graphs.

## Plotting¶

The following tutorials present ways to visualize the graphs, such as its adjacency matrix, and graph embeddings.

## Matching¶

The following tutorials demonstrate how to use the graph matching functionality, including an introduction to the module, and how to utilize the seeding feature.

## Subgraph¶

The following tutorial demonstrates how to estimate the signal-subgraph of samples of a graph/class model according to either the coherent or incoherent estimator models.

## Vertex Nomination¶

The following tutorials demonstrate how to use unattributed single graph spectral vertex nomination or vertex nomination via seeded graph matching to find vertices that are related to a given vertex / set of vertices of interest.

## Aligning¶

The following tutorials shows how to align two seperate datasets with each other, for better comparison of the data.

## Connectomics¶

The following tutorials demonstrate how to apply methods in this package to the analysis of connectomics datasets.