Tutorials

Models

The first 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.

The next tutorial demonstrates how to sample graphs of the same degree sequence using degree preserving edge swaps.

• Random Graph Models
• Degree Preserving Edge Swaps

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).

• Erdos-Renyi (ER) Model
• Stochastic Block Model (SBM)
• Mixed Membership Stochastic Blockmodel (MMSBM)
• Random Dot Product Graph (RDPG) Model
• Correlated Graph Pairs
• Correlated Random Dot Product Graph (RDPG) Graph Pair

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.

• Automatic Gaussian Mixture Modeling
• K-Means Clustering

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.

• Adjacency Spectral Embed
• Out-of-Sample (OOS) Embedding
• Covariate-Assisted Embedding
• Multiple Adjacency Spectral Embedding (MASE)
• Omnibus Embedding for 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.

• Testing Symmetry of Two Networks with the Density Test
• Performing the Density Test
• Group connection test
• Latent Position Two-Graph Testing
• Latent Distribution Two-Graph Testing

Plotting

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

• Heatmap: Visualizing a Graph
• Gridplot: Visualize Multiple Graphs
• Pairplot: Visualizing High Dimensional Data
• Matrixplot and Adjplot: Visualize and sort matrices with metadata
• Pairplot with GMM: Visualizing High Dimensional Data and Clustering
• Networkplot: Visualizing 2D Layouts

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.

• Introduction to Graph Matching
• Seeded Graph Matching (SGM)
• Padded Graph Matching

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.

• Signal Subgraph Estimators

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.

• Spectral Vertex Nomination
• Nomination via SGM

Aligning

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

• Aligning

Connectomics

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

• Methods for Multiscale Comparative Connectomics