def testGetAllShortestPaths(self):
g = Graph(4, [(0, 1), (1, 2), (1, 3), (2, 4), (3, 4), (4, 5)],
directed=True)
sps = sorted(g.get_all_shortest_paths(0, 0))
expected = [[0]]
self.assertEqual(expected, sps)
sps = sorted(g.get_all_shortest_paths(0, 5))
expected = [[0, 1, 2, 4, 5], [0, 1, 3, 4, 5]]
self.assertEqual(expected, sps)
sps = sorted(g.get_all_shortest_paths(1, 4))
expected = [[1, 2, 4], [1, 3, 4]]
self.assertEqual(expected, sps)
g = Graph.Lattice([5, 5], circular=False)
sps = sorted(g.get_all_shortest_paths(0, 12))
expected = [
[0, 1, 2, 7, 12],
[0, 1, 6, 7, 12],
[0, 1, 6, 11, 12],
[0, 5, 6, 7, 12],
[0, 5, 6, 11, 12],
[0, 5, 10, 11, 12],
]
self.assertEqual(expected, sps)
g = Graph.Lattice([100, 100], circular=False)
sps = sorted(g.get_all_shortest_paths(0, 202))
expected = [
[0, 1, 2, 102, 202],
[0, 1, 101, 102, 202],
[0, 1, 101, 201, 202],
[0, 100, 101, 102, 202],
[0, 100, 101, 201, 202],
[0, 100, 200, 201, 202],
]
self.assertEqual(expected, sps)
g = Graph.Lattice([100, 100], circular=False)
sps = sorted(g.get_all_shortest_paths(0, [0, 202]))
self.assertEqual([[0]] + expected, sps)
g = Graph([(0, 1), (1, 2), (0, 2)])
g.es["weight"] = [0.5, 0.5, 1]
sps = sorted(g.get_all_shortest_paths(0, weights="weight"))
self.assertEqual([[0], [0, 1], [0, 1, 2], [0, 2]], sps)
g = Graph.Lattice([4, 4], circular=False)
g.es["weight"] = 1
g.es[2, 8]["weight"] = 100
sps = sorted(g.get_all_shortest_paths(0, [3, 12, 15],
weights="weight"))
self.assertEqual(20, len(sps))
self.assertEqual(4, sum(1 for path in sps if path[-1] == 3))
self.assertEqual(4, sum(1 for path in sps if path[-1] == 12))
self.assertEqual(12, sum(1 for path in sps if path[-1] == 15))
def testSubgraph(self):
g = Graph.Lattice([10, 10], circular=False, mutual=False)
g.vs["id"] = list(range(g.vcount()))
vs = [0, 1, 2, 10, 11, 12, 20, 21, 22]
sg = g.subgraph(vs)
self.assertTrue(
sg.isomorphic(Graph.Lattice([3, 3], circular=False, mutual=False)))
self.assertTrue(sg.vs["id"] == vs)
def testSubgraphEdges(self):
g = Graph.Lattice([10, 10], circular=False, mutual=False)
g.es["id"] = list(range(g.ecount()))
es = [0, 1, 2, 5, 20, 21, 22, 24, 38, 40]
sg = g.subgraph_edges(es)
exp = Graph.Lattice([3, 3], circular=False, mutual=False)
exp.delete_edges([7, 8])
self.assertTrue(sg.isomorphic(exp))
self.assertTrue(sg.es["id"] == es)
def testBetweennessCentrality(self):
g = Graph.Star(5)
self.assertTrue(g.betweenness() == [6.0, 0.0, 0.0, 0.0, 0.0])
g = Graph(5, [(0, 1), (0, 2), (0, 3), (1, 4)])
self.assertTrue(g.betweenness() == [5.0, 3.0, 0.0, 0.0, 0.0])
self.assertTrue(g.betweenness(cutoff=2) == [3.0, 1.0, 0.0, 0.0, 0.0])
self.assertTrue(g.betweenness(cutoff=1) == [0.0, 0.0, 0.0, 0.0, 0.0])
g = Graph.Lattice([3, 3], circular=False)
self.assertTrue(
g.betweenness(
cutoff=2) == [0.5, 2.0, 0.5, 2.0, 4.0, 2.0, 0.5, 2.0, 0.5])
def sample_bottlenecks_and_variance(n_nodes=100, p=.1, n_iterations=100):
max_d_mins = empty(n_iterations)
var_d_mins = empty(n_iterations)
for i in range(n_iterations):
g = Graph.Lattice([1, n_nodes], 4, directed=True)
g.rewire_edges(p)
d_mins = list(map(lambda n: d_min(g, n), range(len(g.vs))))
max_d_mins[i] = nanmax(d_mins)
var_d_mins[i] = nanvar(d_mins)
return max_d_mins, var_d_mins
def testGetAllSimplePaths(self):
g = Graph.Ring(20)
sps = sorted(g.get_all_simple_paths(0, 10))
self.assertEqual(
[
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
[0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10],
],
sps,
)
g = Graph.Ring(20, directed=True)
sps = sorted(g.get_all_simple_paths(0, 10))
self.assertEqual([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]], sps)
sps = sorted(g.get_all_simple_paths(0, 10, mode="in"))
self.assertEqual([[0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10]], sps)
sps = sorted(g.get_all_simple_paths(0, 10, mode="all"))
self.assertEqual(
[
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
[0, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10],
],
sps,
)
g = Graph.Lattice([4, 4], circular=False)
g = Graph([(min(u, v), max(u, v)) for u, v in g.get_edgelist()],
directed=True)
sps = sorted(g.get_all_simple_paths(0, 15))
self.assertEqual(20, len(sps))
for path in sps:
self.assertEqual(0, path[0])
self.assertEqual(15, path[-1])
curr = path[0]
for next in path[1:]:
self.assertTrue(g.are_connected(curr, next))
curr = next
sns.kdeplot(max_d_mins, var_d_mins)
xlabel(r'$d^*$ (interpreting as $\mu$)' +
'\nLow value, high improvement rate')
ylabel(r'variance of $d_{i}^{min}$ (interpreting as $K$)' +
'\nLow value, low fluctuations')
scatter(max_d_mins, var_d_mins, color='k', s=.5, label='Samples')
title('Random networks with %i nodes and %.1f%% connection probability'
'\n%i samples. Contours: Kernely density estimate' %
(n_nodes, p * 100, n_iterations))
plots.savefig(gcf())
plots.close()
# In[11]:
g = Graph.Lattice([1, 1000], 4, directed=True)
# In[30]:
from igraph import Graph
def d_min(g, n):
if not g.predecessors(n):
return nan
return min(map(lambda x: g.outdegree(x), g.predecessors(n)))
def sample_bottlenecks_and_variance(n_nodes=100, p=.1, n_iterations=100):
max_d_mins = empty(n_iterations)
var_d_mins = empty(n_iterations)
