# 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.