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89 lines
2.3 KiB
89 lines
2.3 KiB
kruskal(1) -- Find the minimum/maximum spanning tree of a graph
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======
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## SYNOPSIS
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`kruskal` <graph_in> [MAX]
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## DESCRIPTION
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`kruskal` computes the minimum (or maximum) spanning tree of
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<graph_in>, using the Kruskal's algorithm. If <grahp_in> is
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unweighted, `kruskal` computes one of the spanning trees of the
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graph. The program prints on output the (weighted) edge list of the
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spanning tree.
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## PARAMETERS
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* <graph_in>:
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undirected input graph (edge list). It must be an existing file.
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* `MAX`:
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If the second (optional) parameter is equal to `MAX`, compute the
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maximum spanning tree. Otherwise, compute the minimum spanning tree.
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## OUTPUT
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The program prints on STDOUT the edge list of the minimum (maximum)
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spannig tree of <graph_in>, in the format:
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i_1 j_1 w_ij_1
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i_2 j_2 w_ij_2
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....
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## EXAMPLES
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To find the minimum spanning tree of the graph `stocks_62_weight.net`
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(the network of stocks in the New York Exchange market) we use the
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command:
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$ kruskal stocks_62_weight.net
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52 53 0.72577357
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43 53 0.72838212
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2 53 0.72907212
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...
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36 53 0.7973488
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53 58 0.79931683
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26 27 0.8029602
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$
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which prints on output the edge list of the minimum spanning tree.
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However, since the weight of each edge in that graph indicates the
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similarity in the behaviour of two stocks, the maximum spanning tree
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contains information about the backbone of similarities among
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stocks. To obtain the maximum spannin tree, we just specify `MAX` as
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second parameter:
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$ kruskal stocks_62_weight.net MAX
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56 58 1.523483
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2 52 1.3826744
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32 51 1.3812241
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...
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33 55 0.86880272
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7 28 0.8631584
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1 53 0.81876166
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$
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## SEE ALSO
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clust_w(1), dijkstra(1), largest_component(1)
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## REFERENCES
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* J\. B. Kruskal. "On the shortest spanning subtree of a graph and the
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traveling sales-man problem". P. Am. Math. Soc. 7 (1956),
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48-48.
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Appendix 20, Cambridge University Press
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(2017)
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* V\. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles,
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Methods and Applications", Chapter 10, Cambridge University Press
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(2017)
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## AUTHORS
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(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 `<v.nicosia@qmul.ac.uk>`.
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