I have a >10k list of (unordered) pairs of numbers. I'd like to classify them into sets of connected pairs either directly or indirectly. I think this corresponds to undirected graph. I'm using python, and tried something like this to represent this structure.
In order to know all the numbers connected to i
, I can examine whether there is a path from i
to j
for all j
in the list except i
. However, with this implementation, the computation time gets too long for the size of list I'm dealing with. Is there a more efficient way to do this? (Or is there an already established python libraries?)
It sounds as though you are interested in computing the connected components of a graph. I would suggest looking into the networkx package and its tools for computing components .
For example, suppose our data is a list of pairs of numbers, each pair representing an edge in the graph:
pairs = [
(1, 2),
(2, 4),
(3, 5),
(2, 5),
(7, 9),
(9, 10),
(8, 7)
]
In the graph represented by these edges, there is a path between any pair of nodes in the set {1, 2, 3, 4, 5}
, and there is also a path between any pair of nodes in {6, 7, 8, 9, 10}
. But there is no path, say, from 5
to 7
. This is to say that there are two connected components in the graph.
To discover these components, we first import networkx
and create a graph:
>>> import networkx as nx
>>> graph = nx.from_edgelist(pairs)
Computing the components is as simple as
>>> list(nx.connected_components(graph))
>>> [{1, 2, 3, 4, 5}, {6, 7, 8, 9, 10}]
nx.connected_components
is a generator, and so here we converted the result into a list in order to show all of the connected components.
We can also find the connected component containing a given node:
>>> nx.node_connected_component(graph, 3)
{1, 2, 3, 4, 5}
We can also quickly count the number of connected components:
>>> nx.number_connected_components(graph)
2
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