Multi-agent systems powered by large language models have achieved strong performance on complex tasks, yet naive collaboration topologies often cause high communication costs and redundant context. Existing methods usually use a fixed communication graph and manage collaboration structure and shared memory in separate modules. Our log analysis of several representative systems shows that this separation leads to multiple copies of the same key facts in dialogue, memory and model inputs. We address this issue with EvoHyper, a framework based on an evolving hypergraph topology for multi-agent collaboration. In EvoHyper, a single hypergraph represents agents and shared memory, and each hyperedge serves as a collaboration unit that binds a group of agents to that shared memory. During execution a controller edits the hypergraph through a small set of predefined evolution operations, so collaboration units can spawn, update and merge as tasks unfold. Experiments on four benchmarks covering mathematical reasoning and code generation show that EvoHyper is (I) high-performing, achieving 3.2% to 7.8% accuracy gains over state-of-the-art methods, (II) efficient, reducing token consumption by up to 23.5%, and (III) adaptive, adjusting topology complexity according to task requirements.