  In the context of quantum gravity, we clarify entanglement calculations on
spin networks: we distinguish the gauge-invariant entanglement between
intertwiners located at the nodes and the entanglement between spin states
located on the network's links. We compute explicitly these two notions of
entanglement between neighboring nodes and show that they are always related to
the typical $\ln(2j+1)$ term depending on the spin $j$ living on the link
between them. This $\ln(2j+1)$ contribution comes from looking at non-gauge
invariant states, thus we interpret it as gauge-breaking and unphysical. In
particular, this confirms that pure spin network basis states do not carry any
physical entanglement, so that true entanglement and correlations in loop
quantum gravity comes from spin or intertwiner superpositions.
