feat: added assortativity measures.

xgi-org · nwlandry · Jun 14, 2022 · Jun 5, 2022 · Jun 5, 2022 · Jun 14, 2022
commit ee06fa94cce362827cfd8419e60fd61858a83d21
diff --git a/xgi/algorithms/__init__.py b/xgi/algorithms/__init__.py
@@ -1,3 +1,4 @@
-from xgi.algorithms import connected
+from xgi.algorithms import assortativity, connected
 
-from .connected import *
+from .assortativity import *
+from .connected import *
diff --git a/xgi/algorithms/assortativity.py b/xgi/algorithms/assortativity.py
@@ -0,0 +1,66 @@
+import numpy as np
+import xgi
+from xgi.exception import XGIError
+from itertools import combinations
+import random
+
+__all__ = [
+    "dynamical_assortativity",
+    "top_2_assortativity",
+    "top_bottom_assortativity",
+    "uniform_assortativity",
+]
+
+def dynamical_assortativity(H):
+    """ Gets the dynamical assortativity of a uniform hypergraph.
+
+    Parameters
+    ----------
+    H : xgi.Hypergraph
+        Hypergraph of interest
+
+    Returns
+    -------
+    _type_
+        _description_
+
+    Raises
+    ------
+    XGIError
+        _description_
+    """
+    if not xgi.is_uniform(H):
+        raise XGIError("Hypergraph must be uniform!")
+
+    k1 = np.mean([H.degree(n) for n in H.nodes])
+    k2 = np.mean([H.degree(n)**2 for n in H.nodes])
+
+    kk1 = np.mean([H.degree(n1)*H.degree(n2) for e in H.edges for n1, n2 in combinations(H.edges.members(e), 2)])
+    return kk1*k1**2/k2**2 - 1
+
+
+def top_2_assortativity(H):
+    degrees = dict(H.degree())
+    k1 = [max((degrees[n] for n in H.edges.members(e))) for e in H.edges]
+    try:
+        k2 = [sorted((degrees[n] for n in H.edges.members(e)))[-2] for e in H.edges]
+    except IndexError:
+        raise XGIError("Hypergraph must not have singleton edges.")
+    return np.corrcoef(k1, k2)[0, 1]
+
+
+def top_bottom_assortativity(H):
+    degrees = dict(H.degree())
+    k1 = [max((degrees[n] for n in H.edges.members(e))) for e in H.edges]
+    k2 = [min((degrees[n] for n in H.edges.members(e))) for e in H.edges]
+    return np.corrcoef(k1, k2)[0, 1]
+
+
+def uniform_assortativity(H):
+    degrees = dict(H.degree())
+    try:
+        k1k2 = [[degrees[n] for n in random.sample(H.edges.members(e), 2)] for e in H.edges]
+    except IndexError:
+        raise XGIError("Hypergraph must not have singleton edges.")
+
+    return np.corrcoef(*k1k2)[0, 1]