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crosscloseness.m

@@ -0,0 +1,21 @@
+function cc = crosscloseness(G,select,d,h)
+%function cc = crosscloseness(G,select,d,h)
+%
+%cc is the generalized average crosscloseness of nodes in a graph 
+%G is a graph
+%select is a vector of zeros and ones
+%d sets the depth of the horizoGal relation
+%   d = 1 siblings
+%   d = 2 first cousins
+%   d = 3 second cousins
+%h is the power of the generalized average
+%   h = 1 arithmetic average
+%   h = 0 geometric average
+%   h = -1 harmonic average
+%
+%23 August 2022, Richard S.J. Tol
+
+crossdist = crossdistance(G,select,d);
+
+cc = sum(crossdist.^h,1)/sum(select);
+cc = cc.^(1/h);

crossdistance.m

@@ -0,0 +1,26 @@
+function cd = crossdistance(G,select,d)
+%function cd = crossdistance(G,select,d)
+%
+%cd is the matrix of horizontal distances between selected nodes of G
+%G is a graph
+%select is a vector of zeros and ones
+%d sets the depth of the horizoGal relation
+%   d = 1 siblings
+%   d = 2 first cousins
+%   d = 3 second cousins
+%
+%23 August 2022, Richard S.J. Tol
+
+in = indegree(G);
+nn = size(G.Nodes,1);
+cd = zeros(nn,nn);
+for i=1:nn-1,
+    if in(i) > 0
+        for j=i+1:nn,
+            if select(i) == 1 | select(j) == 1,
+                cd(i,j) = horzdist(G,G.Nodes{i,:},G.Nodes{j,:},d);
+            end
+        end
+    end
+end
+cd = cd + cd';

harmoniccentrality.m

@@ -1,8 +1,10 @@
 function hc = harmoniccentrality(G,s)
 %hc = harmoniccentrality(G,s)
-%G is a graph, directed or no
-%select is a vector of zeros and ones
+%
+%hc is the harmonic average proximity of all nodes to all nodes in G
+%G is a graph
 %s is an optional string, in for incloseness, out for outcloseness
+%(=default)
 %
 %21 February 2018, Richard S.J. Tol
 

harmonicnobelity.m

@@ -1,11 +1,12 @@
 function hc = harmonicnobelity(G,select,s)
 %hc = nobelity(G,select,s)
-%G is a graph, directed or no
+%
+%hc is the harmonic average proximity of all nodes to selected nodes in G
+%G is a graph
 %select is a vector of zeros and ones
+%if select is a vector of ones, hc is the harmonic centrality measure
 %s is an optional string, in for incloseness, out for outcloseness
 %(=default)
-%hc is the average distance to all nodes in select
-%if select is a vector of ones, hc is the harmonic centrality measure
 %
 %22 March 2022, Richard S.J. Tol
 

holdercentrality.m

@@ -1,10 +1,17 @@
 function hc = holdercentrality(G,h,s)
 %hc = holdercentrality(G,h,s)
-%G is a graph, directed or no
-%select is a vector of zeros and ones
+%
+%hc is the generalized average proximity of all nodes to all nodes in G
+%G is a graph
+%h is power of the generalized average
+%   h=1 arithmetic average
+%   h=0 geometric average
+%   h=-1 harmonic average
+%note that hc is undefined for a unconnnected graph unless h<0
 %s is an optional string, in for incloseness, out for outcloseness
+%(=default)
 %
-%21 February 2018, Richard S.J. Tol
+%23 August 2022, Richard S.J. Tol
 
 n = size(G.Nodes,1);
 dist = distances(G);

holdernobelity.m

@@ -1,13 +1,18 @@
 function hc = holdernobelity(G,select,h,s)
-%hc = nobelity(G,select,s)
-%G is a graph, directed or no
+%hc = holdernobelity(G,select,s)
+%
+%hc is the generalized average proximity of all nodes to selected nodes in G
+%G is a graph
 %select is a vector of zeros and ones
+%h is power of the generalized average
+%   h=1 arithmetic average
+%   h=0 geometric average
+%   h=-1 harmonic average
+%note that hc is undefined for a unconnnected graph unless h<0
 %s is an optional string, in for incloseness, out for outcloseness
 %(=default)
-%hc is the average distance to all nodes in select
-%if select is a vector of ones, hc is the harmonic centrality measure
 %
-%22 March 2022, Richard S.J. Tol
+%23 August 2022, Richard S.J. Tol
 
 n = size(G.Nodes,1);
 dist = distances(G);