We introduce stable graphs as a common generalization of compact generalized
polygons with closed adjacency, stable planes and other types of graphs with
continuous geometric operations; non-bipartite structures like Moore graphs are also
included. Topological and graph-theoretical properties of stable graphs are
established, and generalized polygons are characterized among all stable graphs by
means of topological properties. Some results about Moore graphs, which might help
to find infinite examples, are included.
