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chentao3476铁杆木虫 (著名写手)
would-be Dr. CHEN
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[求助]
The relationship between graph distance and Euclidean distance
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| Hello, everyone. I am a postgraduate student who conducts research on complex networks. Now I have a problem to consult all of you. As is known from the theory of complex networks, a network constitutes nodes and edges. My question is what the relationship is between graph distance of two connected nodes and their Euclidean distance? (For instance, in a random graph, the graph distance (average short path length) of two connected nodes (A and B) is L~ln(N)/ln(pN), where N is the total number of nodes, and p is the connection probability between two connected nodes. What is the Euclidean distance of nodes A and B) Thank you. |
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1) Graph distance and Euclidean distance on the grid http://link.springer.com/chapter/10.1007/978-3-642-46908-4_63 2) The ratio of Euclidean distance to graph distance is between two value, this can be seen in "Graph approximations to geodesics on embedded manifolds" ftp://ftp-sop.inria.fr/prisme/bo ... anifolds/isomap.pdf |
2楼2013-12-03 13:16:01
chentao3476
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3楼2013-12-03 15:13:52