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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, Nick Peterson, Omnomnomnom, T. Bongers, Henry T. Horton Aug 29 '13 at 22:48

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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