igraph (version 1.3.5)

igraph-attribute-combination: How igraph functions handle attributes when the graph changes

Description

Many times, when the structure of a graph is modified, vertices/edges map of the original graph map to vertices/edges in the newly created (modified) graph. For example simplify maps multiple edges to single edges. igraph provides a flexible mechanism to specify what to do with the vertex/edge attributes in these cases.

Predefined combination functions

The following combination behaviors are predefined:

"ignore"

The attribute is ignored and dropped.

"sum"

The sum of the attributes is calculated. This does not work for character attributes and works for complex attributes only if they have a sum generic defined. (E.g. it works for sparse matrices from the Matrix package, because they have a sum method.)

"prod"

The product of the attributes is calculated. This does not work for character attributes and works for complex attributes only if they have a prod function defined.

"min"

The minimum of the attributes is calculated and returned. For character and complex attributes the standard R min function is used.

"max"

The maximum of the attributes is calculated and returned. For character and complex attributes the standard R max function is used.

"random"

Chooses one of the supplied attribute values, uniformly randomly. For character and complex attributes this is implemented by calling sample.

"first"

Always chooses the first attribute value. It is implemented by calling the head function.

"last"

Always chooses the last attribute value. It is implemented by calling the tail function.

"mean"

The mean of the attributes is calculated and returned. For character and complex attributes this simply calls the mean function.

"median"

The median of the attributes is selected. Calls the R median function for all attribute types.

"concat"

Concatenate the attributes, using the c function. This results almost always a complex attribute.

Author

Gabor Csardi

Details

The functions that support the combination of attributes have one or two extra arguments called vertex.attr.comb and/or edge.attr.comb that specify how to perform the mapping of the attributes. E.g. contract contracts many vertices into a single one, the attributes of the vertices can be combined and stores as the vertex attributes of the new graph.

The specification of the combination of (vertex or edge) attributes can be given as

1. a character scalar,

2. a function object or

3. a list of character scalars and/or function objects.

If it is a character scalar, then it refers to one of the predefined combinations, see their list below.

If it is a function, then the given function is expected to perform the combination. It will be called once for each new vertex/edge in the graph, with a single argument: the attribute values of the vertices that map to that single vertex.

The third option, a list can be used to specify different combination methods for different attributes. A named entry of the list corresponds to the attribute with the same name. An unnamed entry (i.e. if the name is the empty string) of the list specifies the default combination method. I.e.

list(weight="sum", "ignore")

specifies that the weight of the new edge should be sum of the weights of the corresponding edges in the old graph; and that the rest of the attributes should be ignored (=dropped).

See Also

graph_attr, vertex_attr, edge_attr on how to use graph/vertex/edge attributes in general. igraph_options on igraph parameters.

Examples

g <- graph( c(1,2, 1,2, 1,2, 2,3, 3,4) )
E(g)$weight <- 1:5

## print attribute values with the graph
igraph_options(print.graph.attributes=TRUE)
igraph_options(print.vertex.attributes=TRUE)
igraph_options(print.edge.attributes=TRUE)

## new attribute is the sum of the old ones
simplify(g, edge.attr.comb="sum")

## collect attributes into a string
simplify(g, edge.attr.comb=toString)

## concatenate them into a vector, this creates a complex
## attribute
simplify(g, edge.attr.comb="concat")

E(g)$name <- letters[seq_len(ecount(g))]

## both attributes are collected into strings
simplify(g, edge.attr.comb=toString)

## harmonic average of weights, names are dropped
simplify(g, edge.attr.comb=list(weight=function(x) length(x)/sum(1/x),
                                name="ignore"))