Thin is a value that the option EdgeStyle can take on in the graph data structure or in ShowGraph.

ThomassenGraph returns a hypotraceable graph, a graph G that has no Hamiltonian path but whose subgraph G - v for every vertex v has a Hamiltonian path.

ToAdjacencyLists[g] constructs an adjacency list representation for graph g. ToAdjacencyLists[g, EdgeWeight] returns an adjacency list representation along with edge weights.

ToAdjacencyMatrix[g] constructs an adjacency matrix representation for graph g. ToAdjacencyMatrix[g, EdgeWeight] returns edge weights as entries of the adjacency matrix with ...

ToCanonicalSetPartition[sp, set] reorders sp into a canonical order with respect to set. ToCanonicalSetPartition[sp] reorders sp into canonical order, assuming that ...

ToOrderedPairs[g] constructs a list of ordered pairs representing the edges of the graph g.

TopologicalSort[g] gives a permutation of the vertices of the directed acyclic graph g such that an edge (i, j) implies that vertex i appears before vertex j.

ToUnorderedPairs[g] constructs a list of unordered pairs representing the edges of graph g. Each edge, directed or undirected, results in a pair in which the smaller vertex ...

TransitiveClosure[g] finds the transitive closure of graph g, the supergraph of g that contains edge {x, y} if and only if there is a path from x to y.

TransitiveReduction[g] finds a smallest graph that has the same transitive closure as g.