From simple calculations to full publishable documents and sophisticated dynamic interfaces, everything you can do with Mathematica's standard interactive interface is done ...
GraphPath[g, start, end] finds a shortest path between vertices start and end in graph g.
WeakComponents[g] gives a list of all weakly connected components in the undirected graph g.
ConnectedComponents[g] gives the connected components of the graph g.ConnectedComponents[g, {v_1, v_2, ...}] gives the connected components that include at least one of the ...
BreadthFirstScan[g, s, {"event_1" -> f_1, "event_2" -> f_2, ...}] performs a breadth-first scan (bfs) of the graph g starting at the vertex s and evaluates f_i whenever ...
GraphLayout is an option to Graph and related functions that specifies what layout to use for graph components and collections of components.
TreeGraph[{v_1, v_2, ...}, {u_1, u_2, ...}] yields a tree where u_i is the predecessor of v_i.TreeGraph[{e_1, e_2, ...}] yields a tree with edges e_j.TreeGraph[{v_1, v_2, ...
PropertyValue[{obj, item}, name] gives the property value associated with name for item in obj.
BarabasiAlbertGraphDistribution[n, k] represents a Barabasi\[Dash]Albert graph distribution for n-vertex graphs where a new vertex with k edges is added at each step.
GridLines is an option for two-dimensional graphics functions that specifies grid lines.