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harmonicnobelity.m

@@ -1,12 +1,13 @@
 function hc = harmonicnobelity(G,select,s)
-%nc = nobelity(G,select)
+%hc = nobelity(G,select,s)
 %G is a graph, directed or no
 %select is a vector of zeros and ones
 %s is an optional string, in for incloseness, out for outcloseness
-%nc is the average distance to all nodes in select
-%if select is a vector of ones, nc is the harmonic centrality measure
+%(=default)
+%hc is the average distance to all nodes in select
+%if select is a vector of ones, hc is the harmonic centrality measure
 %
-%21 February 2018, Richard S.J. Tol
+%22 March 2022, Richard S.J. Tol
 
 n = size(G.Nodes,1);
 dist = distances(G);

holdercentrality.m

@@ -0,0 +1,26 @@
+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
+%s is an optional string, in for incloseness, out for outcloseness
+%
+%21 February 2018, Richard S.J. Tol
+
+n = size(G.Nodes,1);
+dist = distances(G);
+invdist = dist.^h;
+for i=1:n
+    invdist(i,i)=0;
+end
+
+if ~exist('s')
+    hc = (n-1)*sum(invdist,2).^(-1/h);
+elseif s(1)=='o'
+    hc = (n-1)*sum(invdist,2).^(-1/h);
+elseif s(1)=='i'
+    hc = (n-1)*(sum(invdist,1)').^(-1/h);
+else
+    hc = 0;
+end
+
+end

holdernobelity.m

@@ -0,0 +1,37 @@
+function hc = holdernobelity(G,select,h,s)
+%hc = nobelity(G,select,s)
+%G is a graph, directed or no
+%select is a vector of zeros and ones
+%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
+
+n = size(G.Nodes,1);
+dist = distances(G);
+for i=1:n
+    if select(i)==0
+        if ~exist('s')
+            dist(:,i) = inf;
+        elseif s(1)=='o'
+            dist(:,i) = inf;
+        else
+            dist(i,:) = inf;
+        end 
+    end
+end
+invdist = dist.^h;
+for i=1:n
+    invdist(i,i)=0;
+end
+if ~exist('s')
+    hc = (n-1)*sum(invdist,2).^(-1/h);
+elseif s(1)=='o'
+    hc = (n-1)*sum(invdist,2).^(-1/h);
+elseif s(1)=='i'
+    hc = (n-1)*(sum(invdist,1)').^(-1/h);
+else
+    hc = 0;
+end