Movement interactions and the underlying social structure in groups have relevance across many social-living species. Collective motion of groups could be based on an "egalitarian" decision system, but in practice it is often influenced by underlying social network structures and by individual characteristics. We investigated whether dominance rank and personality traits are linked to leader and follower roles during joint motion of family dogs. We obtained high-resolution spatio-temporal GPS trajectory data (823,148 data points) from six dogs belonging to the same household and their owner during 14 30-40 min unleashed walks. We identified several features of the dogs' paths (e.g., running speed or distance from the owner) which are characteristic of a given dog. A directional correlation analysis quantifies interactions between pairs of dogs that run loops jointly. We found that dogs play the role of the leader about 50-85% of the time, i.e. the leader and follower roles in a given pair are dynamically interchangable. However, on a longer timescale tendencies to lead differ consistently. The network constructed from these loose leader-follower relations is hierarchical, and the dogs' positions in the network correlates with the age, dominance rank, trainability, controllability, and aggression measures derived from personality questionnaires. We demonstrated the possibility of determining dominance rank and personality traits of an individual based only on its logged movement data. The collective motion of dogs is influenced by underlying social network structures and by characteristics such as personality differences. Our findings could pave the way for automated animal personality and human social interaction measurements.