From 462010ccc3b099695be82a1447d9029d55e0ad59 Mon Sep 17 00:00:00 2001
From: Jim Rafferty <j.m.rafferty@swansea.ac.uk>
Date: Tue, 11 Jan 2022 17:21:01 +0000
Subject: [PATCH] Changed the normalisation options for the eigenvector
 centrality.

---
 .../hypergraph_tools.py                       | 37 +++++++++++++++----
 1 file changed, 30 insertions(+), 7 deletions(-)

diff --git a/multimorbidity_hypergraphs/hypergraph_tools.py b/multimorbidity_hypergraphs/hypergraph_tools.py
index 48e6806..f7355ad 100644
--- a/multimorbidity_hypergraphs/hypergraph_tools.py
+++ b/multimorbidity_hypergraphs/hypergraph_tools.py
@@ -578,6 +578,7 @@ def eigenvector_centrality(
             tolerance=1e-6,
             max_iterations=100,
             random_seed=12345,
+            normalisation="elements"
         ):
 
         """
@@ -632,6 +633,13 @@ def eigenvector_centrality(
 
             random_seed : int, optional
                 The random seed to use in generating the initial vector (default: 12345)
+            
+            normalisation : string, optional
+                The method to use for normalising the eigenvector. The options are 
+                "elements" - normalises by the theoretical maximum number of edges in the 
+                graph
+                "unit" - normalises the eigenvector so it has length one. 
+                (default: "elements")
 
         Returns
         -------
@@ -658,6 +666,8 @@ def eigenvector_centrality(
             weight_population = self.edge_weights_pop
             weight_resultant = self.node_weights
             resultant_pop = self.node_weights_pop
+            
+            n_nodes = len(self.node_list)
         elif rep == "dual":
             inc_mat_original = self.incidence_matrix
             old_eigenvector_estimate = rng.random(self.incidence_matrix.shape[0], dtype='float64')
@@ -666,15 +676,14 @@ def eigenvector_centrality(
             weight_population = self.node_weights_pop
             weight_resultant = self.edge_weights
             resultant_pop = self.edge_weights_pop
+            
+            n_nodes = 2 ** len(self.node_list) - len(self.node_list) - 2
         elif rep == "bipartite":
 
             # We treat the bipartite representation differently -
             # the adjacency matrix is sparse, so we can use a sparse matrix
             # datatype and compute the eigevector directly
 
-            #eigenvector_boot = []
-            #eigenvalue_boot = []
-
             inc_mat = self.incidence_matrix
             weight = self.edge_weights
 
@@ -683,10 +692,17 @@ def eigenvector_centrality(
                 weight
             )
 
-            eigenvector = array(eig_vec / eig_vec.sum())
+            if normalisation == "elements":
+                norm_factor = sqrt(2 ** len(self.node_list) - 2)
+            elif normalisation == "unit":
+                norm_factor = norm(eig_vec)
+            else:
+                raise Exception("Normalisation method not supported.")
+
+            eigenvector = array(eig_vec / norm_factor)
             eigenvalue = eig_val
 
-            return eigenvector# , eigenvector_boot.std(axis=0)
+            return eigenvector
 
         else:
             raise Exception("Representation not supported.")
@@ -780,8 +796,15 @@ def eigenvector_centrality(
                 )
 
         eigenvalue = eigenvalue_estimate
-        # we are applying a scaling to the eigenvector here, so in principle the magnitude also has meaning.
-        eigenvector = array(weight_norm * res_weight_norm * new_eigenvector_estimate / norm(new_eigenvector_estimate))
+    
+        if normalisation == "elements":
+            norm_factor = sqrt(n_nodes)
+        elif normalisation == "unit":
+            norm_factor = norm(eig_vec)
+        else:
+            raise Exception("Normalisation method not supported.")        
+        
+        eigenvector = array(new_eigenvector_estimate / norm_factor)
 
         return eigenvector