def lric(graph,
q=20,
dq=None,
group_size=4,
dw=None,
limpath=3,
models='max',
data=False):
if isinstance(models, str):
models = [models]
g = pairwise_inf(GraphQW(graph, q, dq, group_size, dw),
method='LRIC') # evaluate direct influence
if 'pagerank' in models: # calculate LRIC PageRank
ranking = indirect_pagerank(g).aggregate()
g.set_param('lric_pagerank', ranking)
if 'max' in models: # calculate LRIC_Max
ranking = indirect_paths(g, limpath, 0, 2).aggregate()
g.set_param('lric_max', ranking)
if 'maxmin' in models:
ranking = indirect_paths(g, limpath, 0, 1).aggregate()
g.set_param('lric_maxmin', ranking)
if data:
return ranking, g
else:
return ranking
def sric(graph, q=20, dq=None, group_size=4, dw=None, dCoal=None, data=False):
g = pairwise_inf(GraphQW(graph, q, dq, group_size, dw),
method='SRIC') # calculate SRIC graph
ranking = g.aggregate(name='sric') # calculate centrality of each node
if data:
return ranking, g
else:
return ranking
def sric(graph, q=50, dq=None, group_size=4, size=None, data=False):
"""
SRIC centrality
:param graph: (Graph/DiGraph), input graph (NetworkX package)
:param q: (float, optional), quota (threshold of influence) for each node (share of weighted in-degree).
By default q = 50% of node's weighted in-degree.
:param dq: (float/array/dict, optional), predefined fixed threshold value for each node.
:param group_size: (int, optional), maximal group size (cardinality of coalition). By default limcoal = 4.
:param size: (float/array/dict, optional), nodes size (float, array or dictionary).
By default node size is equal to weighted out-degree.
:param data: (bool): logical scalar. If the data arguments is False, then nodes centrality is returned.
Otherwise, centrality and LRIC graph is returned. By default data = false.
:return:
ranking (dict): nodes SRIC centrality (dictionary)
g (GraphQW) - SRIC graph
"""
g = di.pairwise_inf(GraphQW(graph, q, dq, group_size, size), method='SRIC') # calculate SRIC graph
ranking = g.aggregate(name='sric') # calculate centrality of each node
if data:
return ranking, g
else:
return ranking
def lric(graph, q=50, dq=None, group_size=None, size=None, limpath=3, models='max', data=False):
"""
LRIC centrality
:param graph: (Graph/DiGraph), input graph (NetworkX package)
:param q: (float, optional), quota (threshold of influence) for each node (share of weighted in-degree).
By default q = 50% of node's weighted in-degree.
:param dq: (float/array/dict, optional), predefined fixed threshold value for each node.
:param group_size: (int, optional), maximal group size (cardinality of coalition).
:param size: (float/array/dict, optional), nodes size (float, array or dictionary).
By default node size is equal to weighted out-degree.
:param limpath: (int, optional), maximal length of influence.
:param models: (str/array, optional), type of LRIC centrality (max, maxmin, pagerank).
By default models = "max"
:param data: (bool): logical scalar. If the data arguments is False, then nodes centrality is returned.
Otherwise, centrality and LRIC graph is returned. By default data = false.
:return:
ranking (dict): nodes LRIC centrality (dictionary)
g (GraphQW) - LRIC graph
"""
if isinstance(models, str):
models = [models]
if group_size is None:
group_size = len(graph.nodes()) - 1
ranking = dict()
g = di.pairwise_inf(GraphQW(graph, q, dq, group_size, size), method='LRIC') # evaluate direct influence
if 'pagerank' in models: # calculate LRIC PageRank
ranking = ii.indirect_pagerank(g).aggregate()
g.set_param('lric_pagerank', ranking)
if 'max' in models: # calculate LRIC_Max
ranking = ii.indirect_paths(g, limpath, 0, 2).aggregate()
g.set_param('lric_max', ranking)
if 'maxmin' in models:
ranking = ii.indirect_paths(g, limpath, 0, 1).aggregate()
g.set_param('lric_maxmin', ranking)
if data:
return ranking, g
else:
return ranking
def interdependence(graph, q=50, dq=None, group_size=None, size=None, limpath=3, model=3, data=False):
"""
Interdependence centrality
:param graph: (Graph/DiGraph), input graph (NetworkX package)
:param q: (float, optional), quota (threshold of influence) for each node (share of weighted in-degree).
By default q = 50% of node's weighted in-degree.
:param dq: (float/array/dict, optional), predefined fixed threshold value for each node.
:param group_size: (int, optional), maximal group size (cardinality of coalition). By default limcoal = 3.
:param size: (float/array/dict, optional), nodes size (float, array or dictionary).
By default node size is equal to weighted out-degree.
:param limpath: (int, optional), maximal length of influence.
:param model: model of indirect influence (according to the paper), By default model = 4.
:param data: (bool): logical scalar. If the data arguments is False, then nodes centrality is returned.
Otherwise, centrality and LRIC graph is returned. By default data = false.
:return:
ranking (dict): nodes interdependence centrality (dictionary)
g (GraphQW) - interdependence graph
"""
edge_name = 'weight'
if group_size is None:
group_size = len(graph.nodes()) - 1
if isinstance(q, float) or isinstance(q, int) or q is None:
q = [q, q]
if isinstance(dq, dict) or isinstance(dq, float) or isinstance(dq, int) or dq is None:
dq = [dq, dq]
if isinstance(size, dict)or isinstance(size, float) or isinstance(size, int) or size is None:
size = [size, size]
inf_g = di.pairwise_inf(GraphQW(graph, q[0], dq[0], group_size, size[0]), method='LRIC') # define direct influence
dep_g = di.pairwise_inf(GraphQW(nx.reverse(graph), q[1], dq[1],
group_size, size[1]), method='LRIC') # define direct dependence
if model == 1: # model 1: nodes interdependence as aggregation of indirect influences
indirect1 = ii.indirect_paths(inf_g, limpath, 0, 2)
indirect2 = ii.indirect_paths(dep_g, limpath, 0, 2)
for edge in indirect2.edges(data=True):
if indirect1.has_edge(edge[0], edge[1]) and edge[2][edge_name] > indirect1[edge[0]][edge[1]][edge_name]:
indirect1[edge[0]][edge[1]][edge_name] = edge[2][edge_name]
else:
indirect1.add_edge(edge[0], edge[1], weight=edge[2][edge_name])
g = indirect1.copy()
elif model == 2: # model 2: nodes interdependence based on difference of direct influences
for edge in dep_g.edges(data=True):
if inf_g.has_edge(edge[0], edge[1]):
inf_g[edge[0]][edge[1]][edge_name] += edge[2][edge_name]
else:
inf_g.add_edge(edge[0], edge[1], weight=edge[2][edge_name])
for edge in inf_g.edges(data=True):
v = edge[2][edge_name]
if inf_g.has_edge(edge[1], edge[0]):
v -= inf_g[edge[1]][edge[0]][edge_name]
if v >= 0:
inf_g[edge[0]][edge[1]][edge_name] = v
if inf_g.has_edge(edge[1], edge[0]):
inf_g[edge[1]][edge[0]][edge_name] = 0
else:
inf_g[edge[0]][edge[1]]['weight'] = 0
inf_g[edge[1]][edge[0]]['weight'] = (-1 * v)
if inf_g[edge[0]][edge[1]]['weight'] > 1:
inf_g[edge[0]][edge[1]]['weight'] = 1
g = ii.indirect_paths(inf_g, limpath, 0, 2)
elif model == 3: # model 3: nodes interdependence as a search for influential paths
g = ii.indirect_bipath([inf_g, dep_g], ii.create_quality(inf_g, dep_g), limpath)[1]
if data:
return g.aggregate(), g
else:
return g.aggregate()