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Graph and Network Algorithms

Directed and undirected graphs, network analysis

Graphs model the connections in a network and are widely applicable to a variety of physical, biological, and information systems. You can use graphs to model the neurons in a brain, the flight patterns of an airline, and much more. The structure of a graph is comprised of “nodes” and “edges”. Each node represents an entity, and each edge represents a connection between two nodes. For more information, see Directed and Undirected Graphs.


graphGraph with undirected edges
digraphGraph with directed edges
addnodeAdd new node to graph
rmnodeRemove node from graph
addedgeAdd new edge to graph
rmedgeRemove edge from graph
flipedgeReverse edge directions
numnodesNumber of nodes in graph
numedgesNumber of edges in graph
findnodeLocate node in graph
findedgeLocate edge in graph
reordernodesReorder graph nodes
subgraphExtract subgraph
bfsearchBreadth-first graph search
dfsearchDepth-first graph search
centralityMeasure node importance
maxflowMaximum flow in graph
conncompConnected graph components
biconncompBiconnected graph components
condensationGraph condensation
bctreeBlock-cut tree graph
minspantreeMinimum spanning tree of graph
toposortTopological order of directed acyclic graph
isdagDetermine if graph is acyclic
transclosureTransitive closure
transreductionTransitive reduction
isisomorphicDetermine whether two graphs are isomorphic
isomorphismCompute equivalence relation between two graphs
shortestpathShortest path between two single nodes
shortestpathtreeShortest path tree from node
distancesShortest path distances of all node pairs
adjacencyGraph adjacency matrix
incidenceGraph incidence matrix
laplacianGraph Laplacian matrix
degreeDegree of graph nodes
neighborsNeighbors of graph node
nearestNearest neighbors within radius
indegreeIn-degree of nodes
outdegreeOut-degree of nodes
predecessorsNode predecessors
successorsNode successors
plotPlot graph nodes and edges
labeledgeLabel graph edges
labelnodeLabel graph nodes
layoutChange layout of graph plot
highlightHighlight nodes and edges in plotted graph

Using Objects

GraphPlotGraph plot for directed and undirected graphs


GraphPlot PropertiesControl graph plot appearance and behavior


Directed and Undirected Graphs

Introduction to directed and undirected graphs.

Modify Nodes and Edges of Existing Graph

This example shows how to access and modify the nodes and/or edges in a graph or digraph object using the addedge, rmedge, addnode, rmnode, findedge, findnode, and subgraph functions.

Add Graph Node Names, Edge Weights, and Other Attributes

This example shows how to add attributes to the nodes and edges in graphs created using graph and digraph.

Graph Plotting and Customization

This example shows how to plot graphs, and then customize the display to add labels or highlighting to the graph nodes and edges.

Add Node Properties to Graph Plot Data Cursor

This example shows how to customize the GraphPlot data cursor to display extra node properties of a graph.

Visualize Breadth-First and Depth-First Search

This example shows how to define a function that visualizes the results of bfsearch and dfsearch by highlighting the nodes and edges of a graph.

Build Watts-Strogatz Small World Graph Model

This example shows how to construct and analyze a Watts-Strogatz small-world graph.

Use PageRank Algorithm to Rank Websites

This example shows how to use a PageRank algorithm to rank a collection of websites.

Partition Graph with Laplacian Matrix

This example shows how to use the Laplacian matrix of a graph to compute the Fiedler vector.

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