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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.

`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 |

`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 |

GraphPlot Properties | Control 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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