Explore a 55-minute lecture on graphs with convex balls presented by Jérémie Chalopin at the Workshop on Cube Complexes and Combinatorial Geometry. Delve into the characterization and generalization of bridged/systolic graphs, examining local-to-global characterizations and the contractibility of Rips complexes. Discover how groups acting geometrically on these graphs are biautomatic. Learn about convexity in graphs, metric characterizations, and the simple connectivity of triangle-pentagon complexes. Investigate dismantlable graphs, the 2-sided Fellow Traveler Property, and other metric characterizations in this comprehensive mathematical exploration.