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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.

Functions

graph Create undirected graph
digraph Create directed graph
addnode Add new node to graph
rmnode Remove node from graph
addedge Add new edge to graph
rmedge Remove edge from graph
flipedge Reverse edge directions
numnodes Number of nodes in graph
numedges Number of edges in graph
findnode Locate node in graph
findedge Locate edge in graph
reordernodes Reorder graph nodes
subgraph Extract subgraph
bfsearch Breadth-first graph search
dfsearch Depth-first graph search
centrality Measure node importance
maxflow Maximum flow in graph
conncomp Connected graph components
biconncomp Biconnected graph components
condensation Graph condensation
bctree Block-cut tree graph
minspantree Minimum spanning tree of graph
toposort Topological order of directed acyclic graph
isdag Determine if graph is acyclic
transclosure Transitive closure
transreduction Transitive reduction
isisomorphic Determine whether two graphs are isomorphic
isomorphism Compute equivalence relation between two graphs
shortestpath Shortest path between two single nodes
shortestpathtree Shortest path tree from node
distances Shortest path distances of all node pairs
adjacency Graph adjacency matrix
incidence Graph incidence matrix
laplacian Graph Laplacian matrix
degree Degree of graph nodes
neighbors Neighbors of graph node
nearest Nearest neighbors within radius
indegree In-degree of nodes
outdegree Out-degree of nodes
predecessors Node predecessors
successors Node successors
plot Graph plot
labeledge Label graph edges
labelnode Label graph nodes
layout Change layout of graph plot
highlight Highlight nodes and edges in plotted graph

Using Objects

graph Graph with undirected edges
digraph Graph with directed edges
GraphPlot Graph plot for directed and undirected graphs

Properties

GraphPlot Properties Control graph plot appearance and behavior

Topics

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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