def clique_removal(G):
graph = G.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
maxiset = max(isets)
return maxiset, cliques
def clique_removal(G):
r"""Repeatedly remove cliques from the graph.
Results in a $O(|V|/(\log |V|)^2)$ approximation of maximum clique
and independent set. Returns the largest independent set found, along
with found maximal cliques.
Parameters
----------
G : NetworkX graph
Undirected graph
Returns
-------
max_ind_cliques : (set, list) tuple
2-tuple of Maximal Independent Set and list of maximal cliques (sets).
Raises
------
NetworkXNotImplemented
If the graph is directed or is a multigraph.
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
graph = G.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
# Determine the largest independent set as measured by cardinality.
maxiset = max(isets, key=len)
return maxiset, cliques
def traditional_maxclique(G, name=None):
# complement
if name is None:
name = "complement(%s)" % G.name
R = G.fresh_copy()
R.add_nodes_from(G)
R.add_edges_from(((n, n2) for n, nbrs in G.adjacency() for n2 in G
if n2 not in nbrs if n != n2))
graph = G.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
# Determine the largest independent set as measured by cardinality.
maxiset = max(isets, key=len)
return maxiset
def clique_removal(graph):
""" Repeatedly remove cliques from the nxgraph.
Results in a `O(|V|/(\log |V|)^2)` approximation of maximum clique
& independent set. Returns the largest independent set found, along
with found maximal cliques.
Parameters
----------
nxgraph : NetworkX nxgraph
Undirected nxgraph
Returns
-------
max_ind_cliques : (set, list) tuple
Maximal independent set and list of maximal cliques (sets) in the nxgraph.
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
graph = graph.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
maxiset = max(isets)
return maxiset, cliques
def clique_removal(graph):
""" Repeatedly remove cliques from the graph.
Results in a `O(|V|/(\log |V|)^2)` approximation of maximum clique
& independent set. Returns the largest independent set found, along
with found maximal cliques.
Parameters
----------
graph : NetworkX graph
Undirected graph
Returns
-------
max_ind_cliques : (set, list) tuple
Maximal independent set and list of maximal cliques (sets) in the graph.
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
graph = graph.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
maxiset = max(isets)
return maxiset, cliques
def clique_removal(G):
r""" Repeatedly remove cliques from the graph.
Results in a $O(|V|/(\log |V|)^2)$ approximation of maximum clique
and independent set. Returns the largest independent set found, along
with found maximal cliques.
Parameters
----------
G : NetworkX graph
Undirected graph
Returns
-------
max_ind_cliques : (set, list) tuple
2-tuple of Maximal Independent Set and list of maximal cliques (sets).
References
----------
.. [1] Boppana, R., & Halldórsson, M. M. (1992).
Approximating maximum independent sets by excluding subgraphs.
BIT Numerical Mathematics, 32(2), 180–196. Springer.
"""
graph = G.copy()
c_i, i_i = ramsey.ramsey_R2(graph)
cliques = [c_i]
isets = [i_i]
while graph:
graph.remove_nodes_from(c_i)
c_i, i_i = ramsey.ramsey_R2(graph)
if c_i:
cliques.append(c_i)
if i_i:
isets.append(i_i)
# Determine the largest independent set as measured by cardinality.
maxiset = max(isets, key=len)
return maxiset, cliques
def ramsey_text_coloring(text):
textgraph = RecursiveGlossOverlapGraph(text)
print "Ramsey coloring of text graph - (maxclique, maxindependentset):", ramsey_R2(
textgraph[0])
def main():
g = ds.getData(
'/home/ankursarda/Projects/graph-analytics/networkx/data/sample_data2.adj'
)
res = rm.ramsey_R2(g)
print(res)
def ramsey_text_coloring(text): textgraph=RecursiveGlossOverlapGraph(text) print "Ramsey coloring of text graph - (maxclique, maxindependentset):",ramsey_R2(textgraph[0])