def node2node_flow_from_rank(adj, rank):
# Get flow matrix of the network from the PageRank
# and degree of its nodes
N = adj.shape[0]
T = atMatrix.toRightStochastic(adj)
flow = np.zeros((N, N))
for ii in range(N):
for jj in range(N):
flow[ii, jj] = T[ii, jj] * rank[ii]
return flow
def node2node_flow_from_rank(adj, rank):
# Get flow matrix of the network from the PageRank
# and degree of its nodes
N = adj.shape[0]
T = atMatrix.toRightStochastic(adj)
flow = np.zeros((N, N))
for ii in range(N):
for jj in range(N):
flow[ii, jj] = T[ii, jj] * rank[ii]
return flow
def node2com_trans_from_trans(T, member, dist=None, direction='to'):
T = np.matrix(atMatrix.toRightStochastic(T))
N = T.shape[0]
if (dist is None) and (direction == 'from'):
dist = pagerank(T)
dist = np.matrix(dist).reshape(N, 1)
coms = np.unique(member)
ncom = coms.shape[0]
if direction == 'to':
n2c_trans = np.matrix(np.empty((N, ncom)))
elif direction == 'from':
n2c_trans = np.matrix(np.empty((ncom, N)))
for k in range(ncom):
inodes = member == coms[k]
if direction == 'to':
n2c_trans[:, k] = T[:, inodes].sum(1)
elif direction == 'from':
n2c_trans[k, :] = np.multiply(T[inodes, :], np.tile(dist[inodes], (1, N))).sum(0) / dist[inodes].sum()
else:
sys.exit('Direction must be "to" or "from".')
return n2c_trans
def pagerank(T, tol=0, maxiter=0):
N = T.shape[0]
# Get transition matrix
T = atMatrix.toRightStochastic(T)
# Get First Eigen-Vector
x = np.matrix(np.ones((N, )) * 1. / N)
xi = x * T
k = 1
eps = np.abs(xi - x).sum()
iteration = 0
while eps > tol:
x = xi.copy()
xi = x * T
k += 1
eps = np.abs(xi - x).sum()
iteration += 1
if (maxiter > 0) and (iteration >= maxiter):
break
return xi
def node2com_flow_from_trans(T, member, dist=None, direction='to'):
T = np.matrix(atMatrix.toRightStochastic(T))
N = T.shape[0]
if dist is None:
dist = pagerank(T)
dist = np.matrix(dist).reshape(N, 1)
coms = np.unique(member)
ncom = coms.shape[0]
if direction == 'to':
n2c_flow = np.matrix(np.empty((N, ncom)))
elif direction == 'from':
n2c_flow = np.matrix(np.empty((ncom, N)))
for k in range(ncom):
inodes = member == coms[k]
if direction == 'to':
n2c_flow[:, k] = np.multiply(T[:, inodes].sum(1), dist)
elif direction == 'from':
n2c_flow[k, :] = np.multiply(T[inodes, :],
np.tile(dist[inodes], (1, N))).sum(0)
else:
sys.exit('Direction must be "to" or "from".')
return n2c_flow
def pagerank(T, tol=0, maxiter=0):
N = T.shape[0]
# Get transition matrix
T = atMatrix.toRightStochastic(T)
# Get First Eigen-Vector
x = np.matrix(np.ones((N,)) * 1. / N)
xi = x * T
k = 1
eps = np.abs(xi - x).sum()
iteration = 0
while eps > tol:
x = xi.copy()
xi = x * T
k += 1
eps = np.abs(xi - x).sum()
iteration += 1
if (maxiter > 0) and (iteration >= maxiter):
break
return xi
