circuit analysis - In a grid of resistors, does placement of the voltage source affect the nodal resistances?

Does the placement of the voltage source affect resistances in nodes in a grid of resistors?

And if yes, then is there a right way to "generally" analyze the resistances between nodes of such circuit? I.e. without the analysis depending on the voltage source's place, but rather only on the resistors (and location of nodes) themselves. Can one e.g. analyze the resistances of equivalent resistance without considering any particular voltage source?

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A more simple example:

In this circuit, does the resistance between A and B depend on whether you put the voltage source to come in at A and leave at B?

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Some methods for solving these problems are given here:
http://www.rfcafe.com/miscellany/factoids/kirts-cogitations-256.htm