Currently, if you ask for the volume of a set of vertices, but the set includes indices which are greater than the number of vertices in the graph, the code throws an IndexError from somewhere inside the graph code.

This is not totally unreasonable, but it would help debugging this kind of error if it gave a clear error message. Something like: "Vertex set includes indices larger than number of vertices".

@pmacg I've fixed all of your comments. Unfortunately I made a little bit of a mess of my local repository so I've created a new pull request. Hope this isn't too much trouble for you. If you have any more comments please let me know

There should be tools available to visualise the spectrum of a graph - both the eigenvalues themselves and the spectral embedding of the eigenvectors.

It would be useful to construct a graph from the kronecker product of two existing graphs. That is, the adjacency matrix of the new graph is the kronecker product of the adjacency matrices of the input graphs.

At the moment, the weight function on sgtl.graph.Graph() rounds the weight to the nearest integer and returns an int.

This should return a float to allow fractionally weighted edges.

For a large undirected graph generated from the stochastic block model, the generated graph matrices are not always symmetric. For example:

>>> big_graph = sgtl.random.ssbm(1000, 5, 0.8, 0.2)
>>> lap_mat = big_graph.normalised_laplacian_matrix()
>>> lap_mat_dense = lap_mat.toarray()
>>> np.allclose(lap_mat_dense, lap_mat_dense.T)
False

I haven't debugged this yet, but we should certainly be able to assume that the graph matrices are symmetric for an undirected graph.

Given a weighted graph object, the graph.num_edges gives half of the total volume of the graph, rather than the actual number of weighted edges.

This should be replaced with two methods on the object, a num_edges method which gives the number of non-zero elements of the adjacency matrix (corrected for the symmetry) and a graph_volume method which returns the total weight of all the edges in the graph.

Add a method to add two graphs together, equivalent to adding their adjacency matrices.

If the graphs do not have the same number of vertices, then this method should throw a suitable exception.

Consider overloading the '+' operator so that you can write graph3 = graph1 + graph2.

Add the methods

• adjacency_spectrum()
• laplacian_spectrum()
• normalised_laplacian_spectrum()

To the graph object for returning the eigenvalues of the corresponding graph matrices.

The return value of the Graph.bipartiteness() method should display a beta in math mode in the rendered documentation. See the return value of the conductance method for how to do this.

The scipy sparse linear algebra library has recently introduced sparse arrays rather than matrices and is encouraging their use over the matrix types.

This enhancement covers updating SGTL to allow use of either the sparse array or sparse matrix types.

It may be sometimes useful to use graphs with negative weights. The library is not currently designed with this in mind, but many things might 'just work'. This issue covers investigating formally the behaviour of the library on graphs with negative weights.

The 'Getting Started' page of the documentation currently only gives examples of unweighted graphs. It would be nice to also include a weighted example, or at least mention that this is possible.

The following code for generating a graph from the stochastic block model fails with out-of-bounds errors.

import sgtl.random
import numpy as np


def main():
    cluster_sizes = [100, 50, 20, 20, 20]
    p = 0.8
    prob_mat_q = np.asarray([[p,   0.2, 0.5, 0.1, 0.1],
                             [0.2, p,   0.1, 0.6, 0.2],
                             [0.5, 0.1, p,   0.2, 0.1],
                             [0.1, 0.6, 0.2, p,   0.5],
                             [0.1, 0.2, 0.1, 0.5, p]])
    graph = sgtl.random.sbm(cluster_sizes, prob_mat_q)


if __name__ == '__main__':
    main()

Traceback (most recent call last):
  File ".../main.py", line 17, in <module>
    main()
  File ".../main.py", line 13, in main
    graph = sgtl.random.sbm(cluster_sizes, prob_mat_q)
  File ".../venv/lib/python3.8/site-packages/sgtl/random.py", line 179, in sbm
    adj_mat[vertex_1, vertex_2] = 1
  File ".../venv/lib/python3.8/site-packages/scipy/sparse/_lil.py", line 330, in __setitem__
    return self._set_intXint(key[0], key[1], x)
  File ".../venv/lib/python3.8/site-packages/scipy/sparse/_lil.py", line 299, in _set_intXint
    _csparsetools.lil_insert(self.shape[0], self.shape[1], self.rows,
  File "_csparsetools.pyx", line 61, in scipy.sparse._csparsetools.lil_insert
  File "_csparsetools.pyx", line 87, in scipy.sparse._csparsetools.lil_insert
IndexError: column index (240) out of bounds