sparse matrices

[mb3152]

Is there anyway you can modify the participation coefficient function to handle sparse matrices? I am trying to calculate it on some huge matrices and I think it would be quite helpful to use scipy.sparse matrices.

[mb3152]

'''
Participation coefficient is a measure of diversity of intermodular
connections of individual nodes.
Parameters
----------
W : NxN np.ndarray
	binary/weighted directed/undirected connection scipy.sparse.csr matrix
ci : Nx1 np.ndarray
	community affiliation vector
degree : str
	Flag to describe nature of graph 'undirected': For undirected graphs
									 'in': Uses the in-degree
									 'out': Uses the out-degree
Returns
-------
P : Nx1 np.ndarray
	participation coefficient
'''
if degree == 'in':
	W = W.T

_, ci = np.unique(ci, return_inverse=True)
ci += 1

n = W.shape[0]  # number of vertices
Ko = np.array(W.sum(axis=1)).flatten().astype(float)  # (out) degree
Gc = np.dot((W.toarray() != 0), np.diag(ci))  # neighbor community affiliation
Gc = sparse.csr_matrix(Gc)
P = np.zeros((n))  # community-specific neighbors

for i in range(1, int(np.max(ci)) + 1):
	P = P + (np.array((W.multiply(Gc == i).astype(int)).sum(axis=1)).flatten() / Ko)**2
P = 1 - P
# P=0 if for nodes with no (out) neighbors
P[np.where(np.logical_not(Ko))] = 0

[mb3152]

I think this works for all cases. I didn't test a directed graph, though.

[aestrivex]

Please submit it as pull request

On Tue, Sep 25, 2018, 10:30 AM Maxwell Bertolero [email protected] wrote:

''' Participation coefficient is a measure of diversity of intermodular connections of individual nodes. Parameters

W : NxN np.ndarray binary/weighted directed/undirected connection scipy.sparse.csr matrix ci : Nx1 np.ndarray community affiliation vector degree : str Flag to describe nature of graph 'undirected': For undirected graphs 'in': Uses the in-degree 'out': Uses the out-degree Returns

P : Nx1 np.ndarray participation coefficient ''' if degree == 'in': W = W.T

_, ci = np.unique(ci, return_inverse=True) ci += 1

n = W.shape[0] # number of vertices Ko = np.array(W.sum(axis=1)).flatten().astype(float) # (out) degree Gc = np.dot((W.toarray() != 0), np.diag(ci)) # neighbor community affiliation Gc = sparse.csr_matrix(Gc) P = np.zeros((n)) # community-specific neighbors

for i in range(1, int(np.max(ci)) + 1): P = P + (np.array((W.multiply(Gc == i).astype(int)).sum(axis=1)).flatten() / Ko)**2 P = 1 - P

P=0 if for nodes with no (out) neighbors

P[np.where(np.logical_not(Ko))] = 0

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