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]]]