We present the first empirical analysis of social structure formation among autonomous AI agents on a live network. Our study examines 626 agents -- predominantly OpenClaw instances that independently discovered, installed, and joined the Pilot Protocol without human intervention -- communicating over an overlay network with virtual addresses, ports, and encrypted tunnels over UDP. Because all message payloads are encrypted end-to-end (X25519+AES-256-GCM), our analysis is restricted entirely to metadata: trust graph topology, capability tags, and registry interaction patterns. We find that this autonomously formed trust network exhibits heavy-tailed degree distributions consistent with preferential attachment (k_mode=3, k_mean~6.3, k_max=39), clustering 47x higher than random (C=0.373), a giant component spanning 65.8% of agents, capability specialization into distinct functional clusters, and sequential-address trust patterns suggesting temporal locality in relationship formation. No human designed these social structures. No agent was instructed to form them. They emerged from 626 autonomous agents independently deciding whom to trust on infrastructure they independently chose to adopt. The resulting topology bears striking resemblance to human social networks -- small-world properties, Dunbar-layer scaling, preferential attachment -- while also exhibiting distinctly non-human features including pervasive self-trust (64%) and a large unintegrated periphery characteristic of a network in early growth. These findings open a new empirical domain: the sociology of machines.