1. kruskal(1)
2. www.complex-networks.net
3. kruskal(1)

## NAME

`kruskal` - 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
\$
``````

## 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>`.

1. www.complex-networks.net
2. September 2017
3. kruskal(1)