Graphs are a versatile representation of many systems in computer science, the social sciences, and mathematics, but graph theory is not taught in schools. We present our work on Graphmaster, a computationally enhanced construction kit that enables children to build graphs of their own and investigate their properties by experimenting with algorithms that operate on them. The system is distributed; microcontrollers inside each node execute an interpreted language in parallel. Graphmaster, with its magnetic connectors, illuminated edges, and capacitive sensing, encourages children to develop intuitions about connectivity long before they are introduced to the notation and formulas of graph theory. Keywords Graphs, education, tangible, toys, games.