Graphs & Networks

MultigraphQ — framework-wide support for multigraphs

MixedGraphQ — framework-wide support for mixed (directed and undirected) graphs

FindSpanningTree — find a spanning tree (or spanning forest) of a graph

VertexContract  ▪  EdgeContract  ▪  LinkRankCentrality

Visualization

Graph3D — generate 3D layouts for graphs

PerformanceGoal — performance improvements for all graph visualization

GraphLayout — additional planar embedding "TutteEmbedding"

Paths & Connectivity

FindPath — find all paths between two vertices

FindVertexIndependentPaths  ▪  FindEdgeIndependentPaths

KVertexConnectedComponents  ▪  KEdgeConnectedComponents  ▪  KVertexConnectedGraphQ  ▪  KEdgeConnectedGraphQ

Tours & Cycles

FindShortestTour — new and improved capabilities for tours and cycles

FindCycle — find all cycles

FindFundamentalCycles  ▪  EdgeCycleMatrix

Isomorphisms

FindGraphIsomorphism — find several isomorphism mappings between graphs

GraphAutomorphismGroup — the group of all ways to remap vertex indexes

CanonicalGraph — canonical form for graphs

Relations

TransitiveClosureGraph — the transitive closure or reachability graph

TransitiveReductionGraph — the transitive reduction or Hasse diagram

Polynomials

TuttePolynomial — new graph polynomials

ChromaticPolynomial  ▪  FlowPolynomial