Re: Network integrity and non-random removal of nodes

[<sgorman1 () gmu edu>]

> The  supposition  would  be   that  the  remaining  nodes  are  evenly
> distributed around the core so  the percentage of nodes outside of the
> core without connectivity should be roughly the same as the percentage
> of  nodes  removed  from  the  core.  At least  until  the  core  goes
> non-linear...

Is that the supposition stated in the paper?  The reason being it
contradicts quite a bit of similar research.  Nodes inside and outside
of the core do not typically disconnect at the same rate.  Think of it
this way, if a big well connected node goes down the other big conencted
nodes in the core are likely to have an alternate connection to
compensate for the link loss.  Average distance might go up a little
bit, but that is about it.  The nodes outside of the core on the other
hand are much more sparsely connected.  55% of them are trees meaning
that they only have one connection.  There is no back up link, so if
their big hub node goes down they are out of commission.  Hence you
could have large numbers of nodes outside the core disconencted before
you would see any effect inside the core.  By the time the core goes
non-linear the periphery is gonna be long gone and disconnected.  

----- Original Message -----
From: William Waites <ww () styx org>
Date: Thursday, November 21, 2002 7:14 pm
Subject: Re: Network integrity and non-random removal of nodes

> > > > "Sean" ==   <sgorman1 () gmu edu> writes:
>
>    Sean> it says nothing about what will happen to the other 
> 91.7% of
>    Sean> nodes.   Considering that  55%  of the  remaining nodes  are
>    Sean> trees, they will be saying  "Houston we have a problem" well
>    Sean> before 25%.
>
> The  supposition  would  be   that  the  remaining  nodes  are  evenly
> distributed around the core so  the percentage of nodes outside of the
> core without connectivity should be roughly the same as the percentage
> of  nodes  removed  from  the  core.  At least  until  the  core  goes
> non-linear...
>
>    >> It would be  interesting to see what outdegree  looks like 
> as a
>    >> function of rank -- in the paper they give only the maximum and
>    >> average (geo. mean) outdegrees.  Is there also a critical point
>    >> 25% of the way through  the ranking?  Probably not or one would
>    >> expect they'd have mentioned it...
>
> It turns  out that this is  buried in one  of the graphs (fig.  6) and
> does not appear to have any special properties 25% of the way through.
> It does have an inflection point around the 1000th node or so (2.5%).
>
> -w