  The dynamics of supercritical fluids, a state of matter beyond the gas-liquid
critical point, changes from diffusive to oscillatory motions at high pressure.
This transition is believed to occur across a locus of thermodynamic states
called the Frenkel line. The Frenkel line has been extensively investigated
from the viewpoint of the dynamics, but its structural meaning is not still
well understood. This letter interprets the mesoscopic picture of the Frenkel
line entirely based on a topological and geometrical framework. This discovery
makes it possible to understand the mechanism of rigid/non-rigid transition
based not on the dynamics of individual atoms, but on their instantaneous
configurations. The topological classification method reveals that the
percolation of solid-like structures occurs above the rigid-nonrigid crossover
densities.
