Parameters

Description

graph_center computes a center of the graph g i.e. the node for which the largest of the shortest paths to all the other nodes is minimum. The lengths of the arcs are supposed to be integer (and the default value is 1). The output is the value rad of the length of the radius and no which is the node number of the center of the graph.

Examples

ta=[1 1 2 2 2 3 4 5 5 7 8 8 9 10 10 10 10 11 12 13 13 14 15 16 16 17 17];
he=[2 10 3 5 7 4 2 4 6 8 6 9 7 7 11 13 15 12 13  9 14 11 16 1 17 14 15];
g=make_graph('foo',0,17,ta,he);
g.nodes.graphics.x=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642]/2;
g.nodes.graphics.y=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301]/2;
show_graph(g);
[no,rad] = graph_center(g)
hilite_nodes(no);
r1=0;
for k=1:16
 [p,lp] = shortest_path(no,k,g,'arc');  
  if lp>r1 then r1=lp;path=p;end
end
r1
hilite_edges(path)
 
  

See Also

Bibliography

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35, 1994.