Graph

Graph[{e1,e2,…}] yields a graph with edges ej.

Graph[{v1,v2,…},{e1,e2,…}] yields the graph with vertices vi and edges ej. 

Graph[{…,wi[vi,…],…},{…,wj[ej,…],…}] yields a graph with vertex and edge properties defined by the symbolic wrappers wk.

Graph[data] yields a graph from data.

Please visit the official Wolfram Language Reference for more details and examples on core symbols.