Getting Started

Installation

To use SGTL, first install it using pip.

$ pip install sgtl

Quick Start

Creating Graphs

Graphs in the SGTL are represented using their sparse adjacency matrix. To create a new graph, you can use the following pattern.

>>> import scipy
>>> import sgtl
>>> adjacency_matrix = scipy.sparse.csr_matrix([[0, 1, 1, 1], [1, 0, 0, 0], [1, 0, 0, 0], [1, 0, 0, 0]])
>>> graph = sgtl.Graph(adjacency_matrix)
>>> graph.number_of_vertices()
4
>>> graph.number_of_edges()
3

For more information about the Graph class, see sgtl.graph.Graph.

You can also generate some graphs with standard shapes. For example:

>>> import sgtl.graph
>>> graph = sgtl.graph.cycle_graph(5)
>>> graph.adjacency_matrix().toarray()
array([[0., 1., 0., 0., 1.],
       [1., 0., 1., 0., 0.],
       [0., 1., 0., 1., 0.],
       [0., 0., 1., 0., 1.],
       [1., 0., 0., 1., 0.]])

Or, you can load a more complex graph from an edgelist file like this.

>>> import sgtl.graph
>>> graph = sgtl.graph.from_edgelist("my_graph.edgelist")

See the documentation of the sgtl.graph.from_edgelist method for more information on the required format of the edgelist file.

You can also add graphs together, which corresponds to adding their adjacency matrices.

>>> import sgtl.graph
>>> g1 = sgtl.graph.cycle_graph(5)
>>> g2 = sgtl.graph.path_graph(5)
>>> g3 = g1 + g2
>>> g3.adjacency_matrix().toarray()
array([[0., 2., 0., 0., 1.],
       [2., 0., 2., 0., 0.],
       [0., 2., 0., 2., 0.],
       [0., 0., 2., 0., 2.],
       [1., 0., 0., 2., 0.]])

Viewing the spectrum of a graph

Investigating the spectrum of a graph is very simple. For example, you could visualise the spectrum of the tensor product of two graphs like this.

>>> import sgtl.graph
>>> import sgtl.spectrum
>>> g1 = sgtl.graph.cycle_graph(5)
>>> g2 = sgtl.graph.complete_graph(5)
>>> g3 = g1.tensor_product(g2)
>>> spectrum = sgtl.spectrum.normalised_adjacency_spectrum(g3, plot=True)

The stochastic block model

To generate a random graph from the stochastic block model with 1000 vertices and 5 clusters, you can use the following pattern.

>>> import sgtl.random
>>> p = 0.5
>>> q = 0.1
>>> graph = sgtl.random.ssbm(1000, 5, p, q)

For more information about the methods for generating graphs from the stochastic block model, see sgtl.random.

Spectral clustering

Finding clusters in a graph using spectral clustering is as easy as this:

>>> import sgtl.random
>>> import sgtl.clustering
>>> graph = sgtl.random.ssbm(10, 2, 1, 0.1)
>>> clusters = sgtl.clustering.spectral_clustering(graph, 2)
>>> sorted(clusters)
[[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]

For more information, see sgtl.clustering.