From m.rogers at cs.ucl.ac.uk Fri Oct 19 23:49:43 2007 From: m.rogers at cs.ucl.ac.uk (Michael Rogers) Date: 20 Oct 2007 00:49:43 +0100 Subject: [Tech] Topologies of Freenet In-Reply-To: <200710170013.05474.toad@amphibian.dyndns.org> References: <1191071232.6058.15.camel@boulder> <46FE7876.4070707@cs.ucl.ac.uk> <200710170013.05474.toad@amphibian.dyndns.org> Message-ID: On Oct 17 2007, Matthew Toseland wrote: > What is mixing? If you take a large number of random walks from randomly chosen nodes, the probability of ending up at each node converges towards what's called the stationary distribution as the walks get longer. If the convergence happens quickly, ie a short random walk is nearly equivalent to an infinitely long random walk, the graph is said to have a fast mixing time. In other words if a graph is fast mixing, the local structure is in some sense a good representation of the global structure. Expander graphs are fast mixing; I'm not sure about the various small world and scale-free models. The Sybilguard paper says that social networks are also fast mixing but I'm not sure whether it cites a source for that claim. Cheers, Michael From hallc at lu.unisi.ch Sat Oct 20 00:48:14 2007 From: hallc at lu.unisi.ch (Cyrus Hall) Date: Sat, 20 Oct 2007 02:48:14 +0200 Subject: [Tech] Topologies of Freenet In-Reply-To: References: <1191071232.6058.15.camel@boulder> <46FE7876.4070707@cs.ucl.ac.uk> <200710170013.05474.toad@amphibian.dyndns.org> Message-ID: <1192841294.18531.18.camel@boulder> On Sat, 2007-10-20 at 00:49 +0100, Michael Rogers wrote: > Expander graphs are fast mixing; I'm not sure about the various small world > and scale-free models. The Sybilguard paper says that social networks are > also fast mixing but I'm not sure whether it cites a source for that claim. Small-world networks can indeed be fast-mixing, but not all of them. Small-world is a broad term, yet most people just seem to refer to the Kleinberg or Watts-Strogatz model as if it refers to a class of graphs with similar properties. I think it would be most interesting if someone took some time and tried to come up with a reasonable taxonomy of the small-world phenomenon. Thanks for the sim reference Michael. I've given up looking at Freenet topologies in my work for now, but maybe I'll come back to it when the paper deadline isn't so near. Cheers, Cyrus From alejandro at mosteo.com Sat Oct 20 11:45:06 2007 From: alejandro at mosteo.com (Jano) Date: Sat, 20 Oct 2007 13:45:06 +0200 Subject: [Tech] Topologies of Freenet References: <1191071232.6058.15.camel@boulder> <46FE7876.4070707@cs.ucl.ac.uk> <200710170013.05474.toad@amphibian.dyndns.org> Message-ID: Michael Rogers wrote: > On Oct 17 2007, Matthew Toseland wrote: >> What is mixing? > > If you take a large number of random walks from randomly chosen nodes, the > probability of ending up at each node converges towards what's called the > stationary distribution as the walks get longer. If the convergence > happens quickly, ie a short random walk is nearly equivalent to an > infinitely long random walk, the graph is said to have a fast mixing time. > In other words if a graph is fast mixing, the local structure is in some > sense a good representation of the global structure. Just saw this paper in the last TOC. I have only read the abstract and not perusing it, but perhaps my be interesting: The Convergence-Guaranteed Random Walk and Its Applications in Peer-to-Peer Networks http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tc/&toc=comp/trans/tc/5555/01/t1toc.xml&DOI=10.1109/TC.2007.70837