Re: Re: Re: Finding Clusters

```I feel I have to remark that with respect to me there is nothing
brilliant in the solution I posted. The idea behind it was the result of
a discussion in this group, many, many years ago, on a similar problem.
But anyway, it is a very beautiful result!

The real brilliant thing is the improvement that was given by Szabolcs
Horvat in [mg104644].

Fred

DrMajorBob wrote:
> Brilliant as usual, Fred.
>
> I did think intervals only needed to overlap to "correspond", whereas your
> solution requires them to share an end-point.
>
> For instance, in this example the first interval is a subset of the second
> interval and overlaps with the third, yet "components' associates it with
> neither.
>
> event = {{1, 2} + 1/2, {1, 3}, {3, 4}, {5, 6}, {7, 8}, {8, 10}};
> components@event
>
> {{1, 3, 4}, {3/2, 5/2}, {5, 6}, {7, 8, 10}}
>
> I can't really guess the OP's intent.
>
> Bobby
>
> On Wed, 04 Nov 2009 00:33:25 -0600, Fred Simons <f.h.simons at tue.nl> wrote:
>
>
>> Here is a very short, very fast but not very simple solution:
>>
>> components[lst_List] := Module[{f},
>>   Do[Set @@ f /@ pair, {pair, lst}];   GatherBy[Union @@ lst, f]]
>>
>> Fred Simons
>> Eindhoven University of Technology
>>
>>> All.
>>>
>>> I have a list which represents some natural event. These events are
>>> listed pair-wise, which corresponds to event happening within certain
>>> time interval from each other, as below
>>>
>>> event={{1,2},{1,3},{3,4},{5,6},{7,8},{8,10}}
>>>
>>> I wish to find a thread of events, i.e. if event A is related to B and
>>> B to C, I wish to group {A,B,C} together. For the example above I
>>> would have
>>>
>>> {{1,2,3,4},{5,6},{7,8,10}}
>>>
>>> This would correspond to do a Graph Plot and identifying the parts
>>> which are disconnected It should be simple but I'm really finding it
>>> troublesome.
>>>
>>>
>>>
>>>
>
>
>

```

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