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This research investigates the use of graphic statics in analyzing the structural geometry of a natural phenomenon to understand their performance and their relevant design parameters. Nature has always been inspiring for designers, engineers, and scientists. Structural systems in nature are constantly evolving to optimize themselves with their boundary conditions and the applied loads. Such phenomena follow certain design rules that are quite challenging for humans to formulate or even comprehend. A dragonfly wing is an instance of a high-performance, lightweight structure that has intrigued many researchers to investigate its geometry and its performance as one of the most light-weight structures designed by nature [1]. There are extensive geometrical and analytical studies on the pattern of the wing, but the driving design logic is not clear. The geometry of the internal members of the dragonfly wings mainly consists of convex cells which may, in turn, represent a compression-only network on a 2D plane. However, this phenomenon has never been geometrically analyzed from this perspective to confirm this hypothesis. In this research, we use the methods of 2D graphic statics to construct the force diagram from the given structural geometry of the wing. We use algebraic and geometric graphic statics to unfold the topological and geometric properties of the form and force diagrams such as the degrees of indeterminacies of the network [2]. We then reconstruct the compression-only network of the wing for more than 300 cases for the same boundary conditions and the edge lengths of the independent edges of the network. Comparing the magnitude of the internal forces of the reconstructed network with the actual structure of the wing using the edge length of the force diagram will shed light on the performance of the structure. Multiple analytical studies will be provided to compare the results in both synthetic and natural networks and drive solid conclusions. The success in predicting the internal force flow in the natural structural pattern using graphic statics will expand the use of these powerful methods in reproducing the exact geometry of the natural structural system for use in many engineering and scientific problems. It will also ultimately help us understand the design parameters and boundary conditions for which nature produces its masterpieces.