Adjacency List

The adjacency list representation of a graph consists of  lists one for each vertex , , which gives the vertices to which  is adjacent. The adjacency lists of a graph  may be computed in the Wolfram Language using

  AdjacencyList[g, #]& /@ VertexList[g]

and a graph may be constructed from adjacency lists  using

  Graph[UndirectedEdge @@@ Union[
      Sort /@ Flatten[
      MapIndexed[{#, #2[[1]]}&, l, {2}],
    1]]]

REFERENCES

Skiena, S. "Adjacency Lists." §3.1.2 in Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, pp. 86-87, 1990.