Randomness plays a key role in the order transition of active matter but has not yet been explicitly considered in pairwise interaction connection. In this paper, we introduce the perception rate $P$ into the Vicsek model as the probability of the interaction connections and model the connections as superposition states. We show that with increasing $P$, the polar order number undergoes an order transition and then saturation. The order transition is a first-order phase transition with band formation, and the effect of $P$ is different from density. The change of the order number is linked with the interaction structure. The order transition, order saturation, and phase separation correspond to different critical changes in the local interaction number. The global interaction structure is further analyzed as a network. The decrease of $P$ is comparable to random edge removal, under which the network experiences modal transitions near the critical points of the order number, and the network exhibits surprising robustness. Our results suggest that random interaction can be a new important factor in active matter models, with potential applications in robotic swarms and social activities.

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• Network structure
• Phase transitions by order
• Living matter & active matter
• Vicsek model