  Negativity is a measure of entanglement that can be used both in pure and
mixed states. The negativity spectrum is the spectrum of eigenvalues of the
partially transposed density matrix, and characterizes the degree and "phase"
of entanglement. For pure states, it is simply determined by the entanglement
spectrum. We use a diagrammatic method complemented by a modification of the
Ford-Fulkerson algorithm to find the negativity spectrum in general random
tensor networks with large bond dimensions. In holography, these describe the
entanglement of fixed-area states. It was found that many fixed-area states
have a negativity spectrum given by a semi-circle. More generally, we find new
negativity spectra that appear in random tensor networks, as well as in phase
transitions in holographic states, wormholes, and holographic states with bulk
matter. The smallest random tensor network is the same as a micro-canonical
version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world
branes. We consider the semi-classical negativity of Hawking radiation and find
that contributions from islands should be included. We verify this in the JT
gravity model, showing the Euclidean wormhole origin of these contributions.
