Network as a Computer: Ranking Paths to Find Flows
We explore a simple mathematical model of network computation, based on Markov chains. Similar models apply to a broad range of computational phenomena, arising in networks of computers, as well as in genetic, and neural nets, in social networks, and so on. The main problem of interaction with such spontaneously evolving computational systems is that the data are not uniformly structured. An interesting approach is to try to extract the semantical content of the data from their distribution among the nodes. A concept is then identified by finding the community of nodes that share it. The task of data structuring is thus reduced to the task of finding the network communities, as groups of nodes that together perform some non-local data processing. Towards this goal, we extend the ranking methods from nodes to paths. This allows us to extract some information about the likely flow biases from the available static information about the network.
KeywordsMarkov Chain Mutual Information Path Network Attraction Bias Capacity Matrix
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- 1.Berners-Lee, T.: Semantic Web road map (October 1998)Google Scholar
- 8.Gyöngyi, Z., Garcia-Molina, H., Pedersen, J.: Combating Web spam with TrustRank. In: VLDB, pp. 576–587 (2004)Google Scholar
- 17.Ollivier, Y., Senellart, P.: Finding related pages using Green measures: An illustration with Wikipedia. In: Proceedings of the 22nd AAAI Conference on Artificial Intelligence, Menlo Park, California, July 2007, pp. 1427–1433. AAAI Press (2007)Google Scholar
- 18.O’Reilly, T.: What is Web 2 (September 2005)Google Scholar
- 19.Page, L., Brin, S., Motwani, R., Winograd, T.: The PageRank citation ranking: Bringing order to the Web. Technical report, Stanford Digital Library Technologies Project (1998)Google Scholar
- 20.Pavlovic, D.: Network as a computer: ranking paths to find flows (February 2008), http://aps.arxiv.org/abs/0802.1306 (Preliminary version of this paper, with proofs)