As of Version 10, all the functionality of the GraphUtilities package is built into the Wolfram System.

GraphUtilities contains a number of functions that are useful for graph theory applications. A native implementation of this functionality has been added to the Wolfram System. While there is some overlap in naming, the native Wolfram System implementation is fundamentally different in many ways.

A graph in GraphUtilities is specified by a rule list {v_i1->v_j1,…}. In the Wolfram System, Graph[{v_i1->v_j1,…}] yields a graph object with edges v_i1->v_j,…. This graph object displays in a notebook as a plot of the graph and can be manipulated via functions. See the Graphs & Networks guide for an overview of the Wolfram System functionality.

The complete list of GraphUtilities functions and the corresponding equivalent functions in the Wolfram System are shown below.

GraphUtilities	Built–in Wolfram Language function
AdjacencyMatrix[g]	AdjacencyMatrix[g]
Bicomponents[g]	KVertexConnectedComponents[g,2]
ClosenessCentrality[g]	ClosenessCentrality[g]
CommunityModularity[g,partition]	GraphAssortativity[g,partition]
CommunityStructureAssignment[g]	FindGraphCommunities[g]
CommunityStructurePartition[g]	FindGraphCommunities[g]
EdgeList[g]	EdgeList[g]
ExpressionTreePlot[e]	TreeForm[e]
FindHamiltonianCycle[g]	FindHamiltonianCycle[g]
GraphCoordinates[g]	GraphEmbedding[g]
GraphCoordinates3D[g]	GraphEmbedding[g]
GraphDistance[g,i,j]	GraphDistance[g,i,j]
GraphDistanceMatrix[g]	GraphDistanceMatrix[g]
GraphPath[g,s,t]	FindShortestPath[g,s,t]
HamiltonianCycles[g]	FindHamiltonianCycle[g]
LinkRankMatrix[g]	LinkRankCentrality[g]
LinkRanks[g]	LinkRankCentrality[g]
MaximalBipartiteMatching[g]	FindIndependentEdgeSet[g]
MaximalIndependentEdgeSet[g]	FindIndependentEdgeSet[g]
MaximalIndependentVertexSet[g]	FindIndependentVertexSet[g]
MinCut[g,k]	FindGraphPartition[g,k]
NeighborhoodSubgraph[g,i,d]	NeighborhoodGraph[g,i,d]
NeighborhoodVertices[g,i,d]	NeighborhoodGraph[g,i,d]
PageRanks[g]	PageRankCentrality[g]
PageRankVector[g]	PageRankCentrality[g]
PseudoDiameter[g]	GraphDiameter[g]
StrongComponents[g]	ConnectedComponents[g]
VertexList[g]	VertexList[g]
WeakComponents[g]	WeaklyConnectedComponents[g]

See the Graphs & Networks guide for an overview of the Wolfram System functionality.