The digital logic rewiring technique has been shown to be one of the most powerful logic transformation methods. It has been proven that rewiring is able to further improve some already excellent results on many EDA problems, ranging from logic minimization, partitioning, FPGA technology mappings to final routings. Previous studies have shown that ATPG-based rewiring is one of the most powerful tools for logic perturbation while a graph-based rewiring engine is able to cover nearly one fifth of the target wires with 50 times runtime speedup. For some problems that only require good-enough and very quick solutions, this new rewiring technique may serve as a useful and more practical alternative. In this work, essential elements in graph-based rewiring such as rewiring patterns, pattern size and locality, etc., have been studied to understand their relationship with rewiring performance. A structural analysis on the target-alternative wire pairs discovered by ATPG-based and graph-based engines has also been conducted to analyze the structural characteristics that favor the identification of alternative wires. We have also developed a hybrid rewiring approach that can take the advantages from both ATPG-based and graph-based rewiring. Experimental results suggest that our hybrid engine is able to achieve about 50% of alternative wire coverage when compared with the state-of-the-art ATPG-based rewiring engine with only 4% of the runtime. Through applying our hybrid rewiring approach to the FGPA technology mapping problem, we could achieve similar depth level and look-up table number reductions with much shorter runtime. This shows that the fast runtime of our hybrid approach does not sacrifice the quality of certain rewiring applications.