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Let's say I have a set of N towns and a road network that connects the towns. I think some towns might an influence on other towns because they meet some criterion. I have a binary indicator of this criterion (e.g., crit==1 or crit==0) for each town.

I want to construct a new variable that is a measure of how much each town might be influenced by it's neighbors, giving more weight to closer towns with a value of crit==1. I could define neighborhood as all towns within D km driving distance or R km radius.

What is the best tool in this case? Conceptually, I thought a spatial weights matrix might be useful, but I don't want a NxN matrix. I want a Nx1 matrix where the vector of values is a measure of how much each town might be influenced by its neighbors.

I created a toy example on GitHub.

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You might want to look into the urban network analysis tool developed by MIT, you can identify the reach of specific features in a network.

http://cityform.mit.edu/projects/urban-network-analysis.html

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    this looks helpful, thanks. gravity in particular. – Eric Green Feb 22 '14 at 1:08

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