Chitrakavya, a distinctive form of Indic visual poetry, embeds poetic texts within images having intricate spatial layouts, such as geometric shapes, artistic work and cultural motifs. Tracing the poetic flow in these non-linear designs challenges human readers leave alone machines. This study proposes graphbased traversal algorithms to model the poetic flow in Odia Chitrakavya, addressing contour-prioritized connectivity, self-loops, sequential transitions, and non-sequential jumps. We introduce five Contour-Prioritized Spatial (CPS) algorithms: CPS-DFS No Memoization, CPS-DFS Memoization, CPS-DFS Prune, Contour-Prioritized Spatial Heuristic-Driven Search (CPS-HDS), and a CPS-DFS + CPS-HDS Hybrid. These algorithms, evaluated on Odia Chitrakavya graphs (up to 104 nodes), incorporate dynamic heuristics (weighted contour distance and shape-based similarity) and CUDA accelerated multi-path exploration. Robustness is tested on error injected graphs with 5–10% missing nodes. The CPS algorithms successfully trace poetic flow, achieving 54–63 sequential steps and 1–10 jumps in a 52-node graph and a target string of length 64, outperforming traditional DFS and BFS (7 steps, no jumps, unable to trace the flow) with runtimes of 0.0016–0.0361 seconds. CUDA parallelization reduces runtimes between 15–30% for 52-node graphs (up to 30% for larger graphs), with the hybrid version achieving 0.0014 seconds. The hybrid algorithm yields 94% path optimality. A publicly available JavaScript-based interactive visualization (referenced in the main text), a standardized Odia Chitrakavya dataset, and accompanying Python source code are provided to support reproducible research. These algorithms are script-independent and can be applied to visual poetry traditions in other languages.