In this paper, we address the problem of computing fixed points of nonexpansive operators in a networked multi-agent setting, where agents collaborate over time-varying networks in real Hilbert spaces using local data. Each agent updates its state using a local nonexpansive operator and a combination of states from the network. Inspired by the classical Halpern iteration and prior works on multi-agent Krasnosel'skiĭ–Mann (KM) iterations, we introduce the Halpern algorithm with static weights (HI-SW), and its more general version, the Halpern iteration with time-varying communication graphs (HI-TV) modeled by a sequence of row-stochastic matrices, which aggregates information via multi-hop propagation using historical matrix products. It is shown that the proposed algorithms converge strongly to a fixed point of the global operator that is the projection of the average of local anchors onto the set of its fixed points. Requiring minimal assumptions, these algorithms offer useful tools for optimization and convex feasibility in networked systems. The theoretical results are illustrated with a few numerical examples.