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In percolation theory there is this idea of a giant component, and I am curious what is known about its algebraic connectivity. I looked on google but I was not able to find anything particularly helpful.

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closed as unclear what you're asking by azimut, Nicholas R. Peterson, Omnomnomnom, T. Bongers, Henry T. Horton Aug 29 '13 at 22:48

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Please elaborate. If I understand correctly, algebraic connectivity is a property of a graph, not of a particular component. Furthermore, since the algebraic connectivity of a graph $G$ is greater than 0 if and only if $G$ is connected, nothing more can be said unless the giant component in fact includes all of the vertices. –  Andrew Uzzell Jan 30 '13 at 16:20