Our study aims to investigate the physical properties of graphyne-based nanostructures, with a particular focus on their magnetic and hysteretic features. We analyze the influence of shape on these properties in an Ising-type graphyne structure using the effective field theory (EFT) method. Our research focuses on the critical and compensation temperatures, coercivity, and remanence of the graphyne structure in different shapes, ranging from alpha (α) to beta (β) to gamma (γ). We use the magnetization curves and hysteresis loops obtained from central and intermediate spins. We also illustrate the behavior of the coercive field and remanent magnetization as well as hysteresis loop the effect of exchange interactions r and s as well as temperature. We observe N- and R- type compensation in the β graphyne, and L- and S- type compensations in the γ graphyne. We also find that the widest hysteresis is observed in γ graphyne.