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.

## 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).

## 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.

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

Vertex, edge and graph attributes `delete_edge_attr()`, `delete_graph_attr()`, `delete_vertex_attr()`, `edge_attr()`, `edge_attr<-()`, `edge_attr_names()`, `graph_attr()`, `graph_attr<-()`, `graph_attr_names()`, `igraph-dollar`, `igraph-vs-attributes`, `set_edge_attr()`, `set_graph_attr()`, `set_vertex_attr()`, `vertex_attr()`, `vertex_attr<-()`, `vertex_attr_names()`

## Author

Gabor Csardi csardi.gabor@gmail.com

## Examples

``````
g <- make_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")
#> IGRAPH 853684d D-W- 4 3 --
#> + attr: weight (e/n)
#> + edges from 853684d:
#> [1] 1->2 2->3 3->4

## collect attributes into a string
simplify(g, edge.attr.comb = toString)
#> IGRAPH ec43f6b D-W- 4 3 --
#> + attr: weight (e/c)
#> + edges from ec43f6b:
#> [1] 1->2 2->3 3->4

## concatenate them into a vector, this creates a complex
## attribute
simplify(g, edge.attr.comb = "concat")
#> IGRAPH 4d34088 D-W- 4 3 --
#> + attr: weight (e/x)
#> + edges from 4d34088:
#> [1] 1->2 2->3 3->4

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

## both attributes are collected into strings
simplify(g, edge.attr.comb = toString)
#> IGRAPH 6d9077a D-W- 4 3 --
#> + attr: weight (e/c), name (e/c)
#> + edges from 6d9077a:
#> [1] 1->2 2->3 3->4

## harmonic average of weights, names are dropped
simplify(g, edge.attr.comb = list(
weight = function(x) length(x) / sum(1 / x),
name = "ignore"
))
#> IGRAPH c9ef14c D-W- 4 3 --
#> + attr: weight (e/n)
#> + edges from c9ef14c:
#> [1] 1->2 2->3 3->4
``````