def dist_to_weights(net,epsilon=0.001):
'''Transforms a distance matrix / network to a weight
matrix / network using the formula W = 1 - D / max(D).
Returns a matrix/network'''
N=len(net._nodes)
if (isinstance(net,pynet.SymmFullNet)):
newmat=pynet.SymmFullNet(N)
else:
newmat=pynet.SymmNet()
edges=list(net.edges)
maxd=0.0
for edge in edges:
if edge[2]>maxd:
maxd=edge[2]
# epsilon trick; lowest weight will be almost but
# not entirely zero
maxd=maxd+epsilon
for edge in edges:
if not(edge[2]==maxd):
newmat[edge[0]][edge[1]]=1-edge[2]/maxd
netext.copyNodeProperties(net,newmat)
return newmat
def dist_to_weights(net, epsilon=0.001):
'''Transforms a distance matrix / network to a weight
matrix / network using the formula W = 1 - D / max(D).
Returns a matrix/network'''
N = len(net._nodes)
if (isinstance(net, pynet.SymmFullNet)):
newmat = pynet.SymmFullNet(N)
else:
newmat = pynet.SymmNet()
edges = list(net.edges)
maxd = 0.0
for edge in edges:
if edge[2] > maxd:
maxd = edge[2]
# epsilon trick; lowest weight will be almost but
# not entirely zero
maxd = maxd + epsilon
for edge in edges:
if not (edge[2] == maxd):
newmat[edge[0]][edge[1]] = 1 - edge[2] / maxd
netext.copyNodeProperties(net, newmat)
return newmat
def collapseBipartiteNet(net,nodesToRemove):
"""
Returns an unipartite projection of a bipartite network.
"""
newNet=pynet.SymmNet()
for node in nodesToRemove:
degree=float(net[node].deg())
for node1 in net[node]:
for node2 in net[node]:
if node1.__hash__()>node2.__hash__():
newNet[node1,node2]=newNet[node1,node2]+1.0/degree
netext.copyNodeProperties(net,newNet)
return newNet
def collapseBipartiteNet(net, nodesToRemove):
"""
Returns an unipartite projection of a bipartite network.
"""
newNet = pynet.SymmNet()
for node in nodesToRemove:
degree = float(net[node].deg())
for node1 in net[node]:
for node2 in net[node]:
if node1.__hash__() > node2.__hash__():
newNet[node1, node2] = newNet[node1, node2] + 1.0 / degree
netext.copyNodeProperties(net, newNet)
return newNet
def mst_kruskal(net,randomize=True,maximum=False):
"""Find a minimum/maximum spanning tree using Kruskal's algorithm
If random is set to true and the mst is not unique, a random
mst is chosen.
>>> t=pynet.SymmNet()
>>> t[1,2]=1
>>> t[2,3]=2
>>> t[3,1]=3
>>> m=mst_kruskal(t)
>>> print m.edges
[[1, 2, 1], [2, 3, 2]]
"""
edges=list(net.edges)
if randomize:
random.shuffle(edges) #the sort has been stable since python version 2.3
edges.sort(lambda x,y:cmp(x[2],y[2]),reverse=maximum)
mst=pynet.SymmNet()
numberOfNodes=len(net)
#ktree=percolator.Ktree(numberOfNodes)
ktree=percolator.Ktree() #just use dict
addedEdges=0
for edge in edges:
if ktree.getParent(edge[0])!=ktree.getParent(edge[1]):
mst[edge[0],edge[1]]=edge[2]
ktree.setParent(edge[0],edge[1])
addedEdges+=1
if addedEdges==numberOfNodes-1:
#the mst is a tree
netext.copyNodeProperties(net,mst)
return mst
# else it is a forest
netext.copyNodeProperties(net,mst)
return mst
def mst_kruskal(net, randomize=True, maximum=False):
"""Find a minimum/maximum spanning tree using Kruskal's algorithm
If random is set to true and the mst is not unique, a random
mst is chosen.
>>> t=pynet.SymmNet()
>>> t[1,2]=1
>>> t[2,3]=2
>>> t[3,1]=3
>>> m=mst_kruskal(t)
>>> print m.edges
[[1, 2, 1], [2, 3, 2]]
"""
edges = list(net.edges)
if randomize:
random.shuffle(
edges) #the sort has been stable since python version 2.3
edges.sort(lambda x, y: cmp(x[2], y[2]), reverse=maximum)
mst = pynet.SymmNet()
numberOfNodes = len(net)
#ktree=percolator.Ktree(numberOfNodes)
ktree = percolator.Ktree() #just use dict
addedEdges = 0
for edge in edges:
if ktree.getParent(edge[0]) != ktree.getParent(edge[1]):
mst[edge[0], edge[1]] = edge[2]
ktree.setParent(edge[0], edge[1])
addedEdges += 1
if addedEdges == numberOfNodes - 1:
#the mst is a tree
netext.copyNodeProperties(net, mst)
return mst
# else it is a forest
netext.copyNodeProperties(net, mst)
return mst
def copyNet(net):
""" Copy a network. Also the node properties are copied.
Parameters
----------
net : any pynet object
The network to be copied.
Return
------
newNet : net.__class__ object
A copy of the network.
"""
newNet = net.__copy__()
netext.copyNodeProperties(net, newNet)
return newNet
def copyNet(net):
""" Copy a network. Also the node properties are copied.
Parameters
----------
net : any pynet object
The network to be copied.
Return
------
newNet : net.__class__ object
A copy of the network.
"""
newNet=net.__copy__()
netext.copyNodeProperties(net,newNet)
return newNet
def local_threshold_by_value(net, threshold):
'''Generates a new network by thresholding the input network.
Inputs: net = network, threshold = threshold value,
mode = 0 (accept weights < threshold), 1 (accept weights > threshold)
Returns a network. Note! threshold is really alpha which is defined in
"Extracting the multiscale backbone of complex weighted networks"
http://www.pnas.org/content/106/16/6483.full.pdf'''
newnet = pynet.SymmNet()
for node in net:
s = net[node].strength()
k = net[node].deg()
for neigh in net[node]:
w = net[node, neigh]
if (1 - w / s)**(k - 1) < threshold:
newnet[node, neigh] = w
netext.copyNodeProperties(net, newnet)
return newnet
def local_threshold_by_value(net,threshold):
'''Generates a new network by thresholding the input network.
Inputs: net = network, threshold = threshold value,
mode = 0 (accept weights < threshold), 1 (accept weights > threshold)
Returns a network. Note! threshold is really alpha which is defined in
"Extracting the multiscale backbone of complex weighted networks"
http://www.pnas.org/content/106/16/6483.full.pdf'''
newnet=pynet.SymmNet()
for node in net:
s=net[node].strength()
k=net[node].deg()
for neigh in net[node]:
w=net[node,neigh]
if (1-w/s)**(k-1)<threshold:
newnet[node,neigh]=w
netext.copyNodeProperties(net,newnet)
return newnet
def threshold_by_value(net, threshold, accept="<", keepIsolatedNodes=False):
'''Generates a new network by thresholding the input network.
If using option keepIsolatedNodes=True, all nodes in the
original network will be included in the thresholded network;
otherwise only those nodes which have links will remain (this
is the default).
Inputs: net = network, threshold = threshold value,
accept = "foobar": accept weights foobar threshold (e.g accept = "<": accept weights < threshold)
Returns a network.'''
newnet = pynet.SymmNet()
edges = list(net.edges)
if accept == "<":
for edge in edges:
if (edge[2] < threshold):
newnet[edge[0], edge[1]] = edge[2]
elif accept == ">":
for edge in edges:
if (edge[2] > threshold):
newnet[edge[0], edge[1]] = edge[2]
elif accept == ">=":
for edge in edges:
if (edge[2] >= threshold):
newnet[edge[0], edge[1]] = edge[2]
elif accept == "<=":
for edge in edges:
if (edge[2] <= threshold):
newnet[edge[0], edge[1]] = edge[2]
else:
raise Exception(
"Parameter 'accept' must be either '<', '>', '<=' or '>='.")
# Add isolated nodes to the network.
if keepIsolatedNodes == True:
for node in net:
if not newnet.__contains__(node):
newnet.addNode(node)
netext.copyNodeProperties(net, newnet)
return newnet
def threshold_by_value(net,threshold,accept="<",keepIsolatedNodes=False):
'''Generates a new network by thresholding the input network.
If using option keepIsolatedNodes=True, all nodes in the
original network will be included in the thresholded network;
otherwise only those nodes which have links will remain (this
is the default).
Inputs: net = network, threshold = threshold value,
accept = "foobar": accept weights foobar threshold (e.g accept = "<": accept weights < threshold)
Returns a network.'''
newnet=pynet.SymmNet()
edges=list(net.edges)
if accept == "<":
for edge in edges:
if (edge[2] < threshold):
newnet[edge[0],edge[1]]=edge[2]
elif accept == ">":
for edge in edges:
if (edge[2] > threshold):
newnet[edge[0],edge[1]]=edge[2]
elif accept == ">=":
for edge in edges:
if (edge[2] >= threshold):
newnet[edge[0],edge[1]]=edge[2]
elif accept == "<=":
for edge in edges:
if (edge[2] <= threshold):
newnet[edge[0],edge[1]]=edge[2]
else:
raise Exception("Parameter 'accept' must be either '<', '>', '<=' or '>='.")
# Add isolated nodes to the network.
if keepIsolatedNodes==True:
for node in net:
if not newnet.__contains__(node):
newnet.addNode(node)
netext.copyNodeProperties(net,newnet)
return newnet
def getSubnet(net,nodes):
"""Get induced subgraph.
Parameters
----------
net: pynet.Net, pynet.SymmNet or pynet.SymmFullNet
The original network.
nodes : sequence
The nodes that span the induces subgraph.
Return
------
subnet : type(net)
The induced subgraph that contains only nodes given in
`nodes` and the edges between those nodes that are
present in `net`. Node properties etc are left untouched.
"""
# Handle both directed and undirected networks.
newnet = type(net)() # Initialize to same type as `net`.
degsum=0
for node in nodes:
degsum += net[node].deg()
newnet.addNode(node)
if degsum >= len(nodes)*(len(nodes)-1)/2:
othernodes=set(nodes)
for node in nodes:
if net.isSymmetric():
othernodes.remove(node)
for othernode in othernodes:
if net[node,othernode]!=0:
newnet[node,othernode]=net[node,othernode]
else:
for node in nodes:
for neigh in net[node]:
if neigh in nodes:
newnet[node,neigh]=net[node,neigh]
netext.copyNodeProperties(net, newnet)
return newnet
def getSubnet(net, nodes):
"""Get induced subgraph.
Parameters
----------
net: pynet.Net, pynet.SymmNet or pynet.SymmFullNet
The original network.
nodes : sequence
The nodes that span the induces subgraph.
Return
------
subnet : type(net)
The induced subgraph that contains only nodes given in
`nodes` and the edges between those nodes that are
present in `net`. Node properties etc are left untouched.
"""
# Handle both directed and undirected networks.
newnet = type(net)() # Initialize to same type as `net`.
degsum = 0
for node in nodes:
degsum += net[node].deg()
newnet.addNode(node)
if degsum >= len(nodes) * (len(nodes) - 1) / 2:
othernodes = set(nodes)
for node in nodes:
if net.isSymmetric():
othernodes.remove(node)
for othernode in othernodes:
if net[node, othernode] != 0:
newnet[node, othernode] = net[node, othernode]
else:
for node in nodes:
for neigh in net[node]:
if neigh in nodes:
newnet[node, neigh] = net[node, neigh]
netext.copyNodeProperties(net, newnet)
return newnet
def collapseIndices(net, returnIndexMap=False):
"""Changes the indices of net to run from 0 to len(net)-1.
"""
newNet = type(net)()
indexmap = {}
index = 0
for i in net:
newNet.addNode(index)
indexmap[i] = index;
index += 1
for edge in net.edges:
i,j,w=edge
newNet[indexmap[i]][indexmap[j]] = w
netext.copyNodeProperties(net,newNet)
if returnIndexMap:
return newNet, indexmap
else:
return newNet
def collapseIndices(net, returnIndexMap=False):
"""Changes the indices of net to run from 0 to len(net)-1.
"""
newNet = type(net)()
indexmap = {}
index = 0
for i in net:
newNet.addNode(index)
indexmap[i] = index
index += 1
for edge in net.edges:
i, j, w = edge
newNet[indexmap[i]][indexmap[j]] = w
netext.copyNodeProperties(net, newNet)
if returnIndexMap:
return newNet, indexmap
else:
return newNet
def snowball(net, seed, depth, includeLeafEdges=False):
"""Snowball sampling
Works for both directed and undirected networks. For directed
networks all edges all followed during the sampling (as opposed to
following only outbound edges).
Parameters
----------
net : pynet.SymmNet or pynet.Net object
The network to be sampled.
seed : int or a sequence of ints
The seed of the snowball, either a single node index or
several indices.
depth : int
The depth of the snowball. Depth 1 corresponds to first
neighbors of the seed only.
includeLeafEdges : bool (default: False)
If True, then the edges between the leaves (i.e. the nodes at
final depth) will also be included in the snowball network. By
default these edges are not included.
Return
------
snowball : pynet.SymmNet or pynet.Net object
The snowball sample, will be of the same type as `net`.
"""
if isinstance(seed, int):
seed = [seed]
toVisit=set(seed)
# Create a network for the sample with the same type as `net`.
newNet=type(net)()
visited=set()
for d in range(1,depth+1):
#print "Depth: ",d," visited ", len(visited)," to visit ", len(toVisit)
visited=visited|toVisit
newToVisit=set()
if len(toVisit) == 0:
break
for nodeIndex in toVisit:
node = net[nodeIndex]
# Go through outbound edges (this equals all neighbors in
# an undirected network.
for outIndex in node.iterOut():
newNet[nodeIndex][outIndex] = net[nodeIndex][outIndex]
if outIndex not in visited:
newToVisit.add(outIndex)
# If we are dealing with a directed network, then we must
# also go through the inbound edges.
if isinstance(net, pynet.Net):
for inIndex in node.iterIn():
newNet[inIndex][nodeIndex] = net[inIndex][nodeIndex]
if inIndex not in visited:
newToVisit.add(inIndex)
# If this is the last depth and `includeLeafEdges` is
# True, we add the edges between the most recently added
# nodes, that is, those currently in the set `newToVisit`.
if d == depth and includeLeafEdges:
for nodeIndex in newToVisit:
node = net[nodeIndex]
for outIndex in node.iterOut():
if outIndex in newToVisit:
newNet[nodeIndex][outIndex] = net[nodeIndex][outIndex]
if isinstance(net, pynet.Net):
for inIndex in node.iterIn():
if inIndex in newToVisit:
newNet[inIndex][nodeIndex] = net[inIndex][nodeIndex]
# The nodes to be visited on the next round are the leaves
# found in the current round.
toVisit=newToVisit
netext.copyNodeProperties(net,newNet)
return newNet
def snowball(net, seed, depth, includeLeafEdges=False):
"""Snowball sampling
Works for both directed and undirected networks. For directed
networks all edges all followed during the sampling (as opposed to
following only outbound edges).
Parameters
----------
net : pynet.SymmNet or pynet.Net object
The network to be sampled.
seed : int or a sequence of ints
The seed of the snowball, either a single node index or
several indices.
depth : int
The depth of the snowball. Depth 1 corresponds to first
neighbors of the seed only.
includeLeafEdges : bool (default: False)
If True, then the edges between the leaves (i.e. the nodes at
final depth) will also be included in the snowball network. By
default these edges are not included.
Return
------
snowball : pynet.SymmNet or pynet.Net object
The snowball sample, will be of the same type as `net`.
"""
if isinstance(seed, int):
seed = [seed]
toVisit = set(seed)
# Create a network for the sample with the same type as `net`.
newNet = type(net)()
visited = set()
for d in range(1, depth + 1):
#print "Depth: ",d," visited ", len(visited)," to visit ", len(toVisit)
visited = visited | toVisit
newToVisit = set()
if len(toVisit) == 0:
break
for nodeIndex in toVisit:
node = net[nodeIndex]
# Go through outbound edges (this equals all neighbors in
# an undirected network.
for outIndex in node.iterOut():
newNet[nodeIndex][outIndex] = net[nodeIndex][outIndex]
if outIndex not in visited:
newToVisit.add(outIndex)
# If we are dealing with a directed network, then we must
# also go through the inbound edges.
if isinstance(net, pynet.Net):
for inIndex in node.iterIn():
newNet[inIndex][nodeIndex] = net[inIndex][nodeIndex]
if inIndex not in visited:
newToVisit.add(inIndex)
# If this is the last depth and `includeLeafEdges` is
# True, we add the edges between the most recently added
# nodes, that is, those currently in the set `newToVisit`.
if d == depth and includeLeafEdges:
for nodeIndex in newToVisit:
node = net[nodeIndex]
for outIndex in node.iterOut():
if outIndex in newToVisit:
newNet[nodeIndex][outIndex] = net[nodeIndex][outIndex]
if isinstance(net, pynet.Net):
for inIndex in node.iterIn():
if inIndex in newToVisit:
newNet[inIndex][nodeIndex] = net[inIndex][
nodeIndex]
# The nodes to be visited on the next round are the leaves
# found in the current round.
toVisit = newToVisit
netext.copyNodeProperties(net, newNet)
return newNet
