EulerianGraphQ[g] yields True if the graph g is Eulerian, and False otherwise.
VertexComponent[g, {v_1, v_2, ...}] gives the vertices in the graph g that have a path to at least one of v_1, v_2, ....VertexComponent[g, {v_1, v_2, ...}, k] gives the ...
LineGraph[g] constructs the line graph of graph g.
ResidualFlowGraph[g, flow] returns the directed residual flow graph for graph g with respect to flow.
VertexStyle is an option and property for Graph and related functions that specifies what style to use for vertices.
VertexInComponent[g, {v_1, v_2, ...}] gives the vertices in the graph g that have a directed path to at least one of v_1, v_2, ....VertexInComponent[g, {v_1, v_2, ...}, k] ...
EdgeShapeFunction is an option and property for Graph and related functions that specifies a function to use to generate primitives for rendering each edge.
KirchhoffMatrix[g] gives the Kirchhoff matrix of the graph g.
DIMACS
(Mathematica Import/Export Format) DIMACS graph data format. Commonly used exchange format for graphs. Stores a single undirected graph. Plain text or binary format. DIMACS is an acronym derived from Discrete ...
EdgeLabels is an option and property for Graph and related functions that specifies what labels and label positions should be used for edges.