GraphStyle is an option to Graph and related objects that specifies styles to use for the different graph elements.
VertexSize is an option and property for Graph and related functions that specifies the size used for vertices.
KirchhoffGraph[kmat] gives the graph with Kirchhoff matrix kmat.KirchhoffGraph[{v_1, v_2, ...}, kmat] gives the graph with vertices v_i and Kirchhoff matrix kmat.
ColorSlider[color] represents a color slider currently set to the color corresponding to color.ColorSlider[Dynamic[color]] uses the dynamically updated current value of ...
SetProperty[{obj, item}, name -> value] sets the property name -> value for item in obj.
Opener
(Built-in Mathematica Symbol) Opener[x] represents an opener with setting x, displayed as OpenerBox[True] when x is True and OpenerBox[False] when x is False. Opener[Dynamic[x]] takes the setting to be ...
VerticalSlider[y] represents a vertical slider at position y with range 0 to 1. VerticalSlider[Dynamic[y]] takes the position to be the dynamically updated current value of ...
PassEventsUp is an option to EventHandler that specifies whether events handled by a particular event handler should be passed up to event handlers in outer expressions.
VertexAdd[g, v] makes a graph by adding the vertex v to the graph g.VertexAdd[g, {v_1, v_2, ...}] adds a collection of vertices to g.
GraphDiameter[g] gives the maximum eccentricity of the vertices in the graph g.