NetBunch/doc/kruskal.md

kruskal(1) -- Find the minimum/maximum spanning tree of a graph

SYNOPSIS

kruskal <graph_in> [MAX]

DESCRIPTION

kruskal computes the minimum (or maximum) spanning tree of <graph_in>, using the Kruskal's algorithm. If <grahp_in> is unweighted, kruskal computes one of the spanning trees of the graph. The program prints on output the (weighted) edge list of the spanning tree.

PARAMETERS

• <graph_in>: undirected input graph (edge list). It must be an existing file.

• MAX: If the second (optional) parameter is equal to MAX, compute the maximum spanning tree. Otherwise, compute the minimum spanning tree.

OUTPUT

The program prints on STDOUT the edge list of the minimum (maximum) spannig tree of <graph_in>, in the format:

    i_1 j_1 w_ij_1
    i_2 j_2 w_ij_2
    ....

EXAMPLES

To find the minimum spanning tree of the graph stocks_62_weight.net (the network of stocks in the New York Exchange market) we use the command:

    $ kruskal stocks_62_weight.net
    52 53 0.72577357
    43 53 0.72838212
    2 53 0.72907212
    ...
    36 53 0.7973488
    53 58 0.79931683
    26 27 0.8029602
    $

which prints on output the edge list of the minimum spanning tree. However, since the weight of each edge in that graph indicates the similarity in the behaviour of two stocks, the maximum spanning tree contains information about the backbone of similarities among stocks. To obtain the maximum spannin tree, we just specify MAX as second parameter:

    $ kruskal stocks_62_weight.net MAX
    56 58 1.523483
    2 52 1.3826744
    32 51 1.3812241
    ...
    33 55 0.86880272
    7 28 0.8631584
    1 53 0.81876166
    $

SEE ALSO

clust_w(1), dijkstra(1), largest_component(1)

REFERENCES

• J. B. Kruskal. "On the shortest spanning subtree of a graph and the traveling sales-man problem". P. Am. Math. Soc. 7 (1956), 48-48.

• V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 20, Cambridge University Press (2017)

• V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 10, Cambridge University Press (2017)

AUTHORS

(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.