components - Find the connected components of a graph
components graph_in [SHOW]
components finds the connected components of the undirected graph
given as input using the Depth-First Search algorithm, and prints the
size of each of them. If the optional second parameter SHOW is
provided, the program dumps on output also the list of nodes belonging
to each component.
input graph (edge list) if equal to - (dash), read the edge list
from STDIN.
If the (optional) second parameter is equal to SHOW, the program
will dump on output the list of all the nodes belonging to each
connected component.
components prints on the standard output the size of all the
connected components of the undirected graph given as input, one per
line:
size_1
size_2
size_3
.....
where size_1 is the size of the first component, size_2 is the
size of the second component, and so on. Notice that the sizes are not
sorted. If SHOW is given, the program shows the list of nodes
belonging to each component, in the format:
size_1: node_1 node_2 node_3 ...
size_2: node_1 node_2 node_3 ...
The following command:
$ components er_1000_5000.txt
1000
$
shows on output the size of the only connected component of the graph
er_1000_5000.txt. In this case the graph has only one connected
component (it is a super-critical Erdos-Renyi random graph with 1000
nodes and 5000 edges). A more interesting example can be obtained
using the graph er_1000_2000.txt:
$ components er_1000_2000.txt
985
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
$
In this case, the graph has 16 connected components: one of those components contains 985 nodes, while the other 15 components consist of isolated nodes. If we want to know who are the nodes belonging to each connected component, we run:
$ components er_1000_2000.txt SHOW
985: 0 1 2 3 4 5 6 7 8 9 10 11 12.....
...
1: 63
1: 75
1: 218
1: 222
1: 368
1: 398
1: 441
1: 566
1: 572
1: 663
1: 715
1: 756
1: 863
1: 883
1: 917
$
If we run:
$ components er_1000_2000.txt SHOW > er_1000_2000.txt_components
the result of components will be saved in the file
er_1000_2000.txt_components.
strong_conn(1), node_components(1), largest_component(1)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Chapter 3, Cambridge University Press (2017)
V. Latora, V. Nicosia, G. Russo, "Complex Networks: Principles, Methods and Applications", Appendix 8, Cambridge University Press (2017)
(c) Vincenzo 'KatolaZ' Nicosia 2009-2017 <v.nicosia@qmul.ac.uk>.