Path is a model for mobile startups, offering the best user interface for social-content creation and a great front end to Facebook. But by no sane metric is Path worth $250 million. Like that matters ...

Rainbow connectivity examines how to assign colours to the edges of a graph so that every pair of vertices is joined by at least one “rainbow path”—a path in which no two edges share the same colour.

The zeta function of a graph, inspired by analogues in number theory and differential geometry, encodes fundamental cycle and path data in a compact analytic form. Its prototypical instance, the Ihara ...