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.

Example plots of undirected and directed graphs

Functions

expand all

Construction

Modify Nodes and Edges

Analyze Structure

Traversals, Shortest Paths, and Cycles

Matrix Representation

Node Information

Visualization

Objects

GraphPlot Graph plot for directed and undirected graphs

Properties

GraphPlot Properties

Graph plot appearance and behavior

Topics

Directed and Undirected Graphs
Introduction to directed and undirected graphs.
Graphs and Matrices
This example shows an application of sparse matrices and explains the relationship between graphs and matrices.
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.
Label Graph Nodes and Edges
This example shows how to add and customize labels on graph nodes and edges.
Add Node Properties to Graph Plot Data Tips
This example shows how to customize GraphPlot data tips 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.

Related Information

Graph and Digraph Classes

Featured Examples

Build Watts-Strogatz Small World Graph Model

Construct and analyze a Watts-Strogatz small-world graph. The Watts-Strogatz model is a random graph that has small-world network properties, such as clustering and short average path length.

Use PageRank Algorithm to Rank Websites

Use a PageRank algorithm to rank a collection of websites. Although the PageRank algorithm was originally designed to rank search engine results, it also can be more broadly applied to the nodes in many different types of graphs. The PageRank score gives an idea of the relative importance of each graph node based on how it is connected to the other nodes.

Partition Graph with Laplacian Matrix

Use the Laplacian matrix of a graph to compute the Fiedler vector. The Fiedler vector can be used to partition the graph into two subgraphs.