  Simulation and its variants (e.g., bisimulation and degree-preserving
simulation) are useful in a wide spectrum of applications. However, all
simulation variants are coarse "yes-or-no" indicators that simply confirm or
refute whether one node simulates another, which limits the scope and power of
their utility. Therefore, it is meaningful to develop a fractional
$\chi$-simulation measure to quantify the degree to which one node simulates
another by the simulation variant $\chi$. To this end, we first present several
properties necessary for a fractional $\chi$-simulation measure. Then, we
present $FSim_\chi$, a general fractional $\chi$-simulation computation
framework that can be configured to quantify the extent of all
$\chi$-simulations. Comprehensive experiments and real-world case studies show
the measure to be effective and the computation framework to be efficient.
