Graph object (Multivariate Analysis Toolbox for Matlab®)

This object describes a mathematical entity known as a (undirected) graph. A graph is written as G(V,E), where V is a set of nodes, and E a set of edges connecting them. In a graph object the nodes are assumed to be indexed by sequential integers, 1, 2, ..., n, with n being the number of nodes and stored at the field named no_nodes. Information about edges is stored in the field weights, which is just the n-by-n matrix W. If W(i,j) is nonzero, this means that an edge exists between nodes i and j. For unweighted graph, W is comprised only from the discrete values 0 and 1. If the graph is weighted, the weight of the edge (i,j) is given by W(i,j).

The nodes may be labeled, and this can be stored in the field node_name. Additionally, nodes can be weighted too, a property sometimes referred to as the node's mass. Therefore, these weights are stored in the field node_mass. The object allows for additional user-defined information to be associated with the node, by the mechanism of "customized fields".

Navigate to:     General Description     Class Structure     Class Construction     Class Functions

Each field can be accessed by the dot (.) operation, or by the GET function. The GET function can work on multiple instances simultaneously. Most fields, except for those that are Dependent, can be modified using the dot (.) operation, or by the SET function.

		Field	Description	Type	Default	Dedicated Get/Set Function
		name	name of object, should be short and used as identifier. This field will never be empty.	string	'unnamed'
		description	verbal description of the class content.	string	''
		source	verbal description of the source of information.	string	''
		type	type of graph.	string	'general graph'
		node_name	names of all nodes.	cell array of strings	{}	nodenames
		node_mass	mass of each node.	double vector	[]
		node_cfield	user-specific node customized fields.	cell array of values	{}
		node_cfield_name	names of node customized fields.	cell array of strings	{}
		weights	symmetric sparse weight matrix.	double matrix	[]
	Dependent	no_nodes	number of nodes in the graph.	integer scalar	0	nonodes
	Dependent	no_node_cfields	number of customized fields.	integer scalar	0
	Dependent	no_edges	number of edges in the graph.	integer vector	0	noedges

Empty instance (scalar)

an empty graph instance, with all fields initialized to their default values.

syntax: gr = graph;

Empty instance (matrix)

an array of empty graph instances.

syntax: gr = graph(size,'size');

Copy constructor

one graph instance is copied into another.

syntax: gr_destination = graph(gr_origin);

Construction by field names

an instance is formed by directly providing field values. Any field which is not dependent is permitted.

syntax: gr = graph(field_name, field_value, ...);

Construction by weights and masses

a graph is uniquely defined by a weight matrix, and a vector of node masses.

syntax: gr = graph(W, M);

Construction from a file

a graph is read from a matrix-market file.

syntax: gr = graph(filename);

Computations:

laplacian

computes the Laplacian of a graph.

Customized fields manipulations:

alloccfield

allocates a new customized field to a graph.

cfieldexist

finds whether a customized field exists in a graph.

cfieldnames

lists the customized fields in a GRAPH object.

getcfield

retrieves a customized field from a graph.

setcfield

sets values for a customized field of GRAPHs.

Display:

show

displays class content.

Information extraction:

nodeid

finds the IDs of a list of nodes.

Maintenance:

verify

computes missing fields.

SET/GET functions:

get

get method

nodenames

retrieves the name of the nodes in the graph.

noedges

retrieves the number of edges in GRAPH objects.

nonodes

retrieves the number of nodes in GRAPH objects.

set

set method

Transformations:

swap

replaces the indices of two nodes.

Visualization:

eigenproj

computes the eigenprojection of a graph.