Modular robots form autonomous distributed systems in which modules use communications to coordinate their activities in order to achieve common goals. The complexity of distributed algorithms is generally expressed as a function of network properties, e.g., the number of nodes, the number of links and the radius/diameter of the system. In this paper, we characterize the networks of some lattice-based modular robots which use only neighbor-to-neighbor communications. We demonstrate that they form sparse and large-diameter networks. Additionally, we provide tight bounds for the radius and the diameter of these networks. We also show that, because of the huge diameter and the huge average distance of massive-scale lattice-based networks, complex distributed algorithms for programmable matter pose a significant design challenge. Indeed, communications over a large number of hops cause, for instance, latency and reliability issues.
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