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Abstract: In this paper, we investigate the impact of network topology characteristics on flocking fragmentation for the multi-robot system under a multi-hop and lossy ad hoc network, including the network’s hop count features and information’s successful transmission probability (STP). More specifically, we first propose a distributed communication-calculation-execution protocol to describe the practical interaction and control process in the ad hoc network based multi-robot system, where the flocking control is realized by a discrete-time Olfati-Saber model incorporating STP-related variables. Then, we develop a fragmentation prediction model (FPM) to formulate the impact of hop count features on fragmentation for specific flocking scenarios. This model identifies the critical system and network features that are associated with fragmentation. Further considering general flocking scenarios affected by both hop count features and STP, we formulate the flocking fragmentation probability (FFP) by a data fitting model based on the back propagation neural network, whose input is extracted from the FPM. The FFP formulation quantifies the impact of key network topology characteristics on fragmentation phenomena. Simulation results verify the effectiveness and accuracy of the proposed prediction model and FFP formulation, and several guidelines for constructing the multi-robot ad hoc network are also concluded.