With flexibility in optical layer, elastic optical network (EON) has been considered as a competitive candidate to architect next-generation backbone networks. Routing and spectrum assignment (RSA) is a key problem for the service provisioning in EONs. The RSA problem is NP-hard even in elastic optical rings. Numerous heuristics have been proposed, and they can generally be categorized into two types: Route-First (RF) and Spectrum-First (SF). Although most previous work demonstrated by numerical simulations that the SF algorithms always outperform the RF ones, there is a lack of theoretical analysis on the reasons causing the performance difference between the two types of RSA algorithms. In this paper, we aim at proposing a unified theoretical framework for the performance analysis of RSA algorithms by leveraging conflict graphs, which offers a new perception on the optimality of RSA algorithms. To validate the proposed framework, we apply it in elastic optical rings (with cycle topology), and theoretically analyze the number of edges of the conflict graphs for RF and SF algorithms. Different from the literature, we obtain an interesting observation that neither the RF nor the SF can surpass the other in elastic optical rings under different traffic distributions, and their performances have a strong correlation to the edge count of their conflict graph. This observation provides a new perspective, i.e., conflict graph, to explore the property of RSA algorithms.