A Framework to Quantify Approximate Simulation on Graph Data

TL;DR

This paper introduces a fractional simulation measure for graph nodes, enabling quantification of simulation degrees rather than binary outcomes, with an efficient computation framework validated by experiments.

Contribution

It proposes a novel fractional $ ext{chi}$-simulation measure and a flexible framework for its computation, enhancing the utility of simulation in graph analysis.

Findings

The measure effectively quantifies simulation degrees.

The framework is computationally efficient.

Experiments validate the approach's effectiveness.

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 $\chi$-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.