Event cameras, with microsecond temporal resolution and high dynamic range (HDR) characteristics, emit high-speed event stream for perception tasks. Despite the recent advancement in GNN-based perception methods, they are prone to use straightforward pairwise connectivity mechanisms in the pure Euclidean space where they struggle to capture long-range dependencies and fail to effectively characterize the inherent hierarchical structures of non-uniformly distributed event stream. To this end, in this paper we propose a novel approach named EHGCN, which is a pioneer to perceive event stream in both Euclidean and hyperbolic spaces for event vision. In EHGCN, we introduce an adaptive sampling strategy to dynamically regulate sampling rates, retaining discriminative events while attenuating chaotic noise. Then we present a Markov Vector Field (MVF)-driven motion-aware hyperedge generation method based on motion state transition probabilities, thereby eliminating cross-target spurious associations and providing critically topological priors while capturing long-range dependencies between events. Finally, we propose a Euclidean-Hyperbolic GCN to fuse the information locally aggregated and globally hierarchically modeled in Euclidean and hyperbolic spaces, respectively, to achieve hybrid event perception. Experimental results on event perception tasks such as object detection and recognition validate the effectiveness of our approach.