Generalized node-edge centrality (#165)

Added lambda function default arguments for $f$, $g$, $\varphi$, $\psi$ as defined by Tudisco and Higham. Default behavior is identical as before.

xgi/algorithms/centrality.py

@@ -157,13 +157,33 @@ def apply(H, x, g=lambda v, e: np.sum(v[list(e)])):
     return new_x
 
 
-def node_edge_centrality(H, max_iter=100, tol=1e-6):
+def node_edge_centrality(
+    H,
+    f=lambda x: np.power(x, 2),
+    g=lambda x: np.power(x, 0.5),
+    phi=lambda x: np.power(x, 2),
+    psi=lambda x: np.power(x, 0.5),
+    max_iter=100,
+    tol=1e-6,
+):
     """Computes the node and edge centralities
 
     Parameters
     ----------
     H : Hypergraph
         The hypergraph of interest
+    f : lambda function, default: x^2
+        The function f as described in Tudisco and Higham.
+        Must accept a numpy array.
+    g : lambda function, default: x^0.5
+        The function g as described in Tudisco and Higham.
+        Must accept a numpy array.
+    phi : lambda function, default: x^2
+        The function phi as described in Tudisco and Higham.
+        Must accept a numpy array.
+    psi : lambda function, default: x^0.5
+        The function psi as described in Tudisco and Higham.
+        Must accept a numpy array.
     max_iter : int, default: 100
         Number of iterations at which the algorithm terminates
         if convergence is not reached.
@@ -199,12 +219,9 @@ def node_edge_centrality(H, max_iter=100, tol=1e-6):
 
     check = np.inf
 
-    f = lambda x: np.power(x, 2)
-    g = lambda x: np.power(x, 0.5)
-
     for iter in range(max_iter):
         u = np.multiply(x, g(I * f(y)))
-        v = np.multiply(y, g(I.T * f(x)))
+        v = np.multiply(y, psi(I.T * phi(x)))
         new_x = u / norm(u)
         new_y = v / norm(v)
 

xgi/stats/edgestats.py

@@ -18,6 +18,8 @@
 
 """
 
+import numpy as np
+
 import xgi
 
 __all__ = [
@@ -180,7 +182,16 @@ def size(net, bunch, degree=None):
         }
 
 
-def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
+def node_edge_centrality(
+    net,
+    bunch,
+    f=lambda x: np.power(x, 2),
+    g=lambda x: np.power(x, 0.5),
+    phi=lambda x: np.power(x, 2),
+    psi=lambda x: np.power(x, 0.5),
+    max_iter=100,
+    tol=1e-6,
+):
     """Computes edge centralities.
 
     Parameters
@@ -189,6 +200,18 @@ def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
         The hypergraph of interest
     bunch : Iterable
         Edges in `net`
+    f : lambda function, default: x^2
+        The function f as described in Tudisco and Higham.
+        Must accept a numpy array.
+    g : lambda function, default: x^0.5
+        The function g as described in Tudisco and Higham.
+        Must accept a numpy array.
+    phi : lambda function, default: x^2
+        The function phi as described in Tudisco and Higham.
+        Must accept a numpy array.
+    psi : lambda function, default: x^0.5
+        The function psi as described in Tudisco and Higham.
+        Must accept a numpy array.
     max_iter : int, default: 100
         Number of iterations at which the algorithm terminates
         if convergence is not reached.
@@ -215,5 +238,5 @@ def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
     Francesco Tudisco & Desmond J. Higham,
     https://doi.org/10.1038/s42005-021-00704-2
     """
-    _, c = xgi.node_edge_centrality(net, max_iter, tol)
+    _, c = xgi.node_edge_centrality(net, f, g, phi, psi, max_iter, tol)
     return {e: c[e] for e in c if e in bunch}

xgi/stats/nodestats.py

@@ -18,6 +18,8 @@
 
 """
 
+import numpy as np
+
 import xgi
 
 __all__ = [
@@ -318,7 +320,16 @@ def hec_centrality(net, bunch, max_iter=10, tol=1e-6):
     return {n: c[n] for n in c if n in bunch}
 
 
-def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
+def node_edge_centrality(
+    net,
+    bunch,
+    f=lambda x: np.power(x, 2),
+    g=lambda x: np.power(x, 0.5),
+    phi=lambda x: np.power(x, 2),
+    psi=lambda x: np.power(x, 0.5),
+    max_iter=100,
+    tol=1e-6,
+):
     """Computes node centralities.
 
     Parameters
@@ -327,6 +338,18 @@ def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
         The hypergraph of interest
     bunch : Iterable
         Edges in `net`
+    f : lambda function, default: x^2
+        The function f as described in Tudisco and Higham.
+        Must accept a numpy array.
+    g : lambda function, default: x^0.5
+        The function g as described in Tudisco and Higham.
+        Must accept a numpy array.
+    phi : lambda function, default: x^2
+        The function phi as described in Tudisco and Higham.
+        Must accept a numpy array.
+    psi : lambda function, default: x^0.5
+        The function psi as described in Tudisco and Higham.
+        Must accept a numpy array.
     max_iter : int, default: 100
         Number of iterations at which the algorithm terminates
         if convergence is not reached.
@@ -355,5 +378,5 @@ def node_edge_centrality(net, bunch, max_iter=100, tol=1e-6):
     Francesco Tudisco & Desmond J. Higham,
     https://doi.org/10.1038/s42005-021-00704-2
     """
-    c, _ = xgi.node_edge_centrality(net, max_iter, tol)
+    c, _ = xgi.node_edge_centrality(net, f, g, phi, psi, max_iter, tol)
     return {n: c[n] for n in c if n in bunch}