A Framework to Quantify Approximate Simulation on Graph Data

Abstract

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 χ-simulation measure to quantify the degree to which one node simulates another by the simulation variant χ. To this end, we first present several properties necessary for a fractional χ-simulation measure. Then, we present FSim χ , a general fractional χ-simulation computation framework that can be configured to quantify the extent of all χ-simulations. Comprehensive experiments and real-world case studies show the measure to be effective and the computation framework to be efficient.1 A node u is an out-neighbor of u, if there is an outgoing edge from u to u in G. Similarly, u is an in-neighbor of u, if an edge from u to u presents.