Social, and other, Networks
Networks can be considered to be very large graphs with several hundreds
The can be undirected (symmetric), directed (asymmetric) or mixed.
While there are many statistical methods of analyzing networks, they
tend to yield only global properties.
Closed set analysis can reveal much finer detail.
One analytic technique is reduction.
All nodes are closed in an irreducible network.
The irreducible ``core'' of any network is unique (upto isomorphism).
In this irreducible core, every node is a part of a chordless circuit of
length 4, or more.
Thus they are the exact antithesis of chordal graphs.
often an order of magnitude smaller.
Consequently, they can be used to identify local network features of interest.
[P11] J.L. Pfaltz,
Mathmetical Continuity in Dynamic Social Networks,
3rd International Conf. on Social Informatics, SOCINFO 2011 ,
LNCS #6984, 36-50.
[P12a] J.L. Pfaltz,
Finding the Mule in the Network,
ASONAM 2012, Intern. Conf on Advances in Social Network Analysis and Mining,
[P12b] J.L. Pfaltz,
Entropy in Social Networks,
SocInfo 2012, Intern. Conf on Social Informatics ,
[P12c] J.L. Pfaltz and Josef Slapal,
Transformations of discrete closure systems,
Acta Math. Hungar.
Sept. 2012 (electronic version), March 2013 (print version).
[P17] J.L. Pfaltz,
A Category of "Undirected Graphs": A Tribute to Hartmut Ehrig,