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I have a question regarding the delocalised electron in graphite. There has been conflicting information between books.

Some books said the delocalised electron in graphite exists $\bf{between}$ layers. Some said the delocalised electron in graphite exists $\bf{within}$ the hexagonal layer.

I support the second statement, because carbon has electronic configuration of 1s2 2s2 2p2. Graphite has sp2, therefore leaves 1 p orbital. And the giant pi bond should be extended over the layer, instead of between.

I am not sure my evidence is sound. Any advice would be greatly appreciated. Thank you in advance.

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It's just a matter of definition. If a "layer" is understood as an infinitely thin plane passing through the centers of carbon atoms, then the electron density of the huge delocalized $\pi$ orbital is located above and below that plane, i.e., technically between layers. If a layer is defined so as to include whole atoms, then the said orbital is within layer.

In any case, the delocalized electrons are more or less "free" to move along the planes and not perpendicular to them, which explains the high anisotropy in electrical conductance and other properties of graphite.

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