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chentao3476

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would-be Dr. CHEN

[ÇóÖú] The relationship between graph distance and Euclidean distance

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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feixiaolin

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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
2Â¥2013-12-03 13:16:01
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chentao3476

Ìú¸Ëľ³æ (ÖøÃûдÊÖ)

would-be Dr. CHEN

Thank you, so much
My dream sheds lights on me
3Â¥2013-12-03 15:13:52
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