# Cohesion of Simplicial Complexes

Right, so that gives rise to description of simplicial complexes in terms of cohesion

http://www.afscet.asso.fr/resSystemica/Crete02/Legrand.pdf

http://en.wikipedia.org/wiki/Simplicial_complex has a generalization of the original Ronald H Atkin (1965... 19 q-Analysis reviewed at http://www.springerlink.com/content/m3131024x3482452/fulltext.pdf where (simplicial) q-connectivity is defined... Your distinction "the three nodes attended one event or because they jointly attended three events pairwise, in the first that single event would disconnect, in the second no single event can disconnect" is decribed in Atkin's formalism.

Jeff Johnson at open university continues to pursue this approach http://design.open.ac.uk/johnson/publications.htm Not for network analysis but for design....

http://en.wikipedia.org/wiki/Abstract_simplicial_complex http://en.wikipedia.org/wiki/Kruskal-Katona_theorem

http://planetmath.org/encyclopedia/SimplicialComplex.html Doug 13:22, 8 January 2008 (PST) (reply to Jim)

On Tue, 8 Jan 2008, James Moody wrote:

> Date: Tue, 08 Jan 2008 13:48:23 -0500 > From: James Moody <jmoody77@soc.duke.edu> > To: Doug White <drwhite@uci.edu> > Subject: Re: Nice use of 4-clique percolation > > Hmm. My intuition is that since there are multiple 2-mode networks that will give rise to the same 1-mode network, that these two wouldn't necessarily be equivalent.

> That is , since we can see a 3-clique in a network because the three nodes attended one event or because they jointly attended three events pairwise, in the first that single event would disconnect, in the second no single event can disconnect.