# Elementary Invariants of a Graph

## `Order(G): Grph -> RngIntElt`

## `NumberOfVertices(G): Grph -> RngIntElt`

The number of vertices of the graph $G$.

## `Size(G): Grph -> RngIntElt`

## `NumberOfEdges(G): Grph -> RngIntElt`

The number of edges of the graph $G$.

## `CharacteristicPolynomial(G): GrphUnd -> RngUPolElt`

The characteristic polynomial (over the integers) of the graph $G$; i.e. the characteristic polynomial of the adjacency matrix of $G$.

## `Spectrum(G): GrphUnd -> SetEnum`

The spectrum of the graph $G$; i.e. the roots of the characteristic polynomial of $G$. The roots are returned as a set of tuples, each containing a root and its multiplicity.