What does it mean by grouping by connected components?

Jun 26, 2012 at 10:47 AM
Dear all, I would like to find out the meaning of grouping by connected components. The write up in the nodeXL says to group the graph's vertices  into Strongly connected components. In this case, is nodeXL getting their common characteristics based on the graph's metrics ( vertices's centrality, egienvector, closeness, betweeness eg to group upon? Algorithm? I was being asked this question and had read on Internet and discussion threads on this but by far hasn't gotten much insightful answers. Thanks all Cody
Coordinator
Jun 26, 2012 at 12:14 PM

Hello!

A single connected component can be thought of as an island of nodes.  Sometimes the island is continental in size (Australia?).

A connected component is defined as a collection of connected nodes.  A graph has two connected components when two connected collections of nodes have zero connections to one another.  

When you group by connected components the result could be thought of as an archipelago of connected nodes.

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Marc

Jun 26, 2012 at 3:18 PM

Hey Marc,

I still dont quite get it at the 2nd paragraph.

What I could interpret from there is that the 2 connected collections of nodes are not linked by any of the nodes
in the collections thus having 0 connections to each other.

So my graph has 393 connected component groupings, does that mean they are all collections of nodes that have no connections to each other?

Then how do you determine them together as a collection?

Thank you.

Cody

Coordinator
Jun 26, 2012 at 3:23 PM

Each isolated node is its own connected component, an island, albeit a small one.

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Marc

Jun 26, 2012 at 3:44 PM
Edited Jun 26, 2012 at 3:54 PM

I'll also quote from the "Creating Groups by Connected Component" topic at NodeXL, Help, Help:

"A connected component is a set of vertices that are connected to each other but not to the rest of the graph."
...
"An isolate is a one-vertex connected component and is thus put into its own group."

-- Tony

Jun 27, 2012 at 12:24 AM

Hi Marc & Tony ,

Thanks very much for the replies. Ok, a set of vertices that are connected to each other . Do this set of vertices have something in common ? Or they just happen to be near each other to be grouped together in connected component.


Thank you


Cody

Coordinator
Jun 27, 2012 at 12:39 AM
Hello!

A connected component is not composed of nodes that are near one another, they are composed of nodes that are *connected* to one another by whatever edges your data contains.

Marc

On Jun 26, 2012, at 5:24 PM, "cody_q" <notifications@codeplex.com> wrote:

From: cody_q

Hi Marc & Tony ,

Thanks very much for the replies. Ok, a set of vertices that are connected to each other . Do this set of vertices have something in common ? Or they just happen to be near each other to be grouped together in connected component.


Thank you


Cody

Jun 27, 2012 at 12:48 AM

http://en.wikipedia.org/wiki/Connected_component_(graph_theory)