Improve analyses of very large graphs

analyze.py

@@ -200,7 +200,17 @@ def get_tgap(g):
     if 2 >= g.num_vertices() - 1:
         return numpy.nan
     T = transition(g, operator=True)
-    ew = scipy.sparse.linalg.eigs(T, k=2, which="LR", return_eigenvectors=False)
+    k = numpy.array(g.degree_property_map("out").fa, dtype="float")
+    k /= numpy.linalg.norm(k)
+    def matvec(x):
+        return T.matvec(x) - numpy.dot(k, x) * k
+    Tp = scipy.sparse.linalg.LinearOperator(T.shape, matvec=matvec)
+    try:
+        ew = scipy.sparse.linalg.eigs(Tp, k=1, which="LR",
+                                      return_eigenvectors=False,
+                                      tol=1e-6)
+    except scipy.sparse.linalg.eigen.arpack.ArpackNoConvergence:
+        return numpy.nan
     return float(min(ew.real))
 
 @register("mixing_time", "Random walk mixing time", "log")
@@ -215,17 +225,20 @@ def get_mixing(g, tgap):
 @cache_result
 def get_hgap(g):
     g = GraphView(g, directed=False)
-    remove_parallel_edges(g)
+    l = label_parallel_edges(g, mark_only=True)
+    if l.fa.max() > 0:
+        l.a = numpy.logical_not(l.a)
+        g = GraphView(g, efilt=l)
+    else:
+        del l
     T = hashimoto(g, compact=True, operator=True)
     try:
         ew = scipy.sparse.linalg.eigs(T, k=1, which="LR", return_eigenvectors=False)
-    except TypeError:
+    except (TypeError, scipy.sparse.linalg.eigen.arpack.ArpackNoConvergence):
         return numpy.nan
-    finally:
-        g.clear()
     return float(ew.real[0])
 
-@register("diameter", "(Pseudo-) diameter")
+@register("diameter", "(Pseudo-) diameter", "log")
 @cache_result
 def get_diameter(g):
     g = GraphView(g, directed=False)
@@ -255,7 +268,7 @@ def get_vprops(g):
     return vprops
 
 @register("pos")
-@restrict(N=10000000, exclude=["openstreetmap"])
+@restrict(N=1000000, exclude=["openstreetmap"])
 @cache_result
 def get_pos(g):
     if g.num_vertices() < 1000: