def complement(G):
"""
Returns the complement of Graph G
Parameters
----------
G : A directed staticgraph
Returns
-------
H : A new staticgraph graph.
Notes
------
It is mandatory that G be directed.
"""
nset = set(G.nodes())
n_nodes = G.order()
n_edges = n_nodes * (n_nodes - 1) - G.size() + 1
cmp_edges = ((u, v) for u in G.nodes()
for v in nset - set(G.successors(u)))
deg = make_deg(n_nodes, cmp_edges)
cmp_edges = ((u, v) for u in G.nodes()
for v in nset - set(G.successors(u)))
H = make(n_nodes, n_edges, cmp_edges, deg)
return H
def union(G, H):
"""
Return a new graph which is the simple union
of the node sets and edge sets.
Parameters
----------
G,H : Two directed simple staticgraph
Returns
-------
GC: A new graph with the same type as G
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
edges = ((u, v) for u in G.nodes()
for v in chain(G.successors(u), H.successors(u)))
deg = make_deg(n_nodes, edges)
edges = ((u, v) for u in G.nodes()
for v in chain(G.successors(u), H.successors(u)))
GC = make(n_nodes, G.size() + H.size(), edges, deg)
return GC
def intersection(G, H):
"""
Return a new graph that contains only the edges that exist in
both G and H.
The node sets of H and G must be the same.
Parameters
----------
G,H : Two directed simple staticgraphs
Returns
-------
GH : A new graph with the same type as G.
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
edges = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) & set(H.successors(u)))
deg = make_deg(n_nodes, edges)
edges = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) & set(H.successors(u)))
GH = make(n_nodes, G.size(), edges, deg)
return GH
def complement(G):
"""
Returns the complement of Graph G
Parameters
----------
G : A directed staticgraph
Returns
-------
H : A new staticgraph graph.
Notes
------
It is mandatory that G be directed.
"""
nset = set(G.nodes())
n_nodes = G.order()
n_edges = n_nodes * (n_nodes - 1) - G.size() + 1
cmp_edges = ((u, v) for u in G.nodes()
for v in nset - set(G.successors(u)))
deg = make_deg(n_nodes, cmp_edges)
cmp_edges = ((u, v) for u in G.nodes()
for v in nset - set(G.successors(u)))
H = make(n_nodes, n_edges, cmp_edges, deg)
return H
def intersection(G, H):
"""
Return a new graph that contains only the edges that exist in
both G and H.
The node sets of H and G must be the same.
Parameters
----------
G,H : Two directed simple staticgraphs
Returns
-------
GH : A new graph with the same type as G.
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
edges = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) & set(H.successors(u)))
deg = make_deg(n_nodes, edges)
edges = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) & set(H.successors(u)))
GH = make(n_nodes, G.size(), edges, deg)
return GH
def union(G, H):
"""
Return a new graph which is the simple union
of the node sets and edge sets.
Parameters
----------
G,H : Two directed simple staticgraph
Returns
-------
GC: A new graph with the same type as G
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
edges = ((u, v) for u in G.nodes()
for v in chain(G.successors(u), H.successors(u)))
deg = make_deg(n_nodes, edges)
edges = ((u, v) for u in G.nodes()
for v in chain(G.successors(u), H.successors(u)))
GC = make(n_nodes, G.size() + H.size(), edges, deg)
return GC
def symmetric_difference(G, H):
"""
Return new graph with edges that exist in either G or H but not both.
The node sets of H and G must be the same.
Parameters
----------
G,H : Two directed simple staticgraphs
Returns
-------
D : A new graph with the same type as G.
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
diff1 = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) - set(H.successors(u)))
diff2 = ((u, v) for u in H.nodes()
for v in set(H.successors(u)) - set(G.successors(u)))
edges = chain(diff1, diff2)
deg = make_deg(n_nodes, edges)
diff1 = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) - set(H.successors(u)))
diff2 = ((u, v) for u in H.nodes()
for v in set(H.successors(u)) - set(G.successors(u)))
edges = chain(diff1, diff2)
D = make(n_nodes, G.size() + H.size(), edges, deg)
return D
def symmetric_difference(G, H):
"""
Return new graph with edges that exist in either G or H but not both.
The node sets of H and G must be the same.
Parameters
----------
G,H : Two directed simple staticgraphs
Returns
-------
D : A new graph with the same type as G.
Notes
-----
It is mandatory that G and H be both directed.
The node sets of G and H must be same.
"""
if G.order() != H.order():
msg = "Node sets of the two directed graphs are not equal!"
raise StaticGraphNotEqNodesException(msg)
n_nodes = G.order()
diff1 = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) - set(H.successors(u)))
diff2 = ((u, v) for u in H.nodes()
for v in set(H.successors(u)) - set(G.successors(u)))
edges = chain(diff1, diff2)
deg = make_deg(n_nodes, edges)
diff1 = ((u, v) for u in G.nodes()
for v in set(G.successors(u)) - set(H.successors(u)))
diff2 = ((u, v) for u in H.nodes()
for v in set(H.successors(u)) - set(G.successors(u)))
edges = chain(diff1, diff2)
D = make(n_nodes, G.size() + H.size(), edges, deg)
return D