These functions find the vertices not farther than a given limit from
another fixed vertex, these are called the neighborhood of the vertex.
Note that `ego()`

and `neighborhood()`

,
`ego_size()`

and `neighborhood_size()`

,
`make_ego_graph()`

and `make_neighborhood()_graph()`

,
are synonyms (aliases).

## Usage

```
connect(graph, order, mode = c("all", "out", "in", "total"))
ego_size(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
neighborhood_size(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
ego(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
neighborhood(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
make_ego_graph(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
make_neighborhood_graph(
graph,
order = 1,
nodes = V(graph),
mode = c("all", "out", "in"),
mindist = 0
)
```

## Arguments

- graph
The input graph.

- order
Integer giving the order of the neighborhood.

- mode
Character constant, it specifies how to use the direction of the edges if a directed graph is analyzed. For ‘out’ only the outgoing edges are followed, so all vertices reachable from the source vertex in at most

`order`

steps are counted. For ‘"in"’ all vertices from which the source vertex is reachable in at most`order`

steps are counted. ‘"all"’ ignores the direction of the edges. This argument is ignored for undirected graphs.- nodes
The vertices for which the calculation is performed.

- mindist
The minimum distance to include the vertex in the result.

## Value

`ego_size()`

/`neighborhood_size()`

returns with an integer vector.`ego()`

/`neighborhood()`

(synonyms) returns A list of`igraph.vs`

or a list of numeric vectors depending on the value of`igraph_opt("return.vs.es")`

, see details for performance characteristics.`make_ego_graph()`

/`make_neighborhood_graph()`

returns with a list of graphs.`connect()`

returns with a new graph object.

## Details

The neighborhood of a given order `r`

of a vertex `v`

includes all
vertices which are closer to `v`

than the order. I.e. order 0 is always
`v`

itself, order 1 is `v`

plus its immediate neighbors, order 2
is order 1 plus the immediate neighbors of the vertices in order 1, etc.

`ego_size()`

/`neighborhood_size()`

(synonyms) returns the size of the neighborhoods of the given order,
for each given vertex.

`ego()`

/`neighborhood()`

(synonyms) returns the vertices belonging to the neighborhoods of the given
order, for each given vertex.

`make_ego_graph()`

/`make_neighborhood()_graph()`

(synonyms) is creates (sub)graphs from all neighborhoods of
the given vertices with the given order parameter. This function preserves
the vertex, edge and graph attributes.

`connect()`

creates a new graph by connecting each vertex to
all other vertices in its neighborhood.

## See also

Other functions for manipulating graph structure:
`+.igraph()`

,
`add_edges()`

,
`add_vertices()`

,
`complementer()`

,
`compose()`

,
`contract()`

,
`delete_edges()`

,
`delete_vertices()`

,
`difference.igraph()`

,
`difference()`

,
`disjoint_union()`

,
`edge()`

,
`igraph-minus`

,
`intersection.igraph()`

,
`intersection()`

,
`path()`

,
`permute()`

,
`rep.igraph()`

,
`reverse_edges()`

,
`simplify()`

,
`union.igraph()`

,
`union()`

,
`vertex()`

Other structural.properties:
`bfs()`

,
`component_distribution()`

,
`constraint()`

,
`coreness()`

,
`degree()`

,
`dfs()`

,
`distance_table()`

,
`edge_density()`

,
`feedback_arc_set()`

,
`girth()`

,
`is_acyclic()`

,
`is_dag()`

,
`is_matching()`

,
`knn()`

,
`laplacian_matrix()`

,
`reciprocity()`

,
`subcomponent()`

,
`subgraph()`

,
`topo_sort()`

,
`transitivity()`

,
`unfold_tree()`

,
`which_multiple()`

,
`which_mutual()`

## Author

Gabor Csardi csardi.gabor@gmail.com, the first version was done by Vincent Matossian

## Examples

```
g <- make_ring(10)
ego_size(g, order = 0, 1:3)
#> [1] 1 1 1
ego_size(g, order = 1, 1:3)
#> [1] 3 3 3
ego_size(g, order = 2, 1:3)
#> [1] 5 5 5
# neighborhood_size() is an alias of ego_size()
neighborhood_size(g, order = 0, 1:3)
#> [1] 1 1 1
neighborhood_size(g, order = 1, 1:3)
#> [1] 3 3 3
neighborhood_size(g, order = 2, 1:3)
#> [1] 5 5 5
ego(g, order = 0, 1:3)
#> [[1]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 1
#>
#> [[2]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 2
#>
#> [[3]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 3
#>
ego(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 1 2 10
#>
#> [[2]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 2 1 3
#>
#> [[3]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 3 2 4
#>
ego(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 1 2 10 3 9
#>
#> [[2]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 2 1 3 10 4
#>
#> [[3]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 3 2 4 1 5
#>
# neighborhood() is an alias of ego()
neighborhood(g, order = 0, 1:3)
#> [[1]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 1
#>
#> [[2]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 2
#>
#> [[3]]
#> + 1/10 vertex, from 30edc7b:
#> [1] 3
#>
neighborhood(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 1 2 10
#>
#> [[2]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 2 1 3
#>
#> [[3]]
#> + 3/10 vertices, from 30edc7b:
#> [1] 3 2 4
#>
neighborhood(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 1 2 10 3 9
#>
#> [[2]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 2 1 3 10 4
#>
#> [[3]]
#> + 5/10 vertices, from 30edc7b:
#> [1] 3 2 4 1 5
#>
# attributes are preserved
V(g)$name <- c("a", "b", "c", "d", "e", "f", "g", "h", "i", "j")
make_ego_graph(g, order = 2, 1:3)
#> [[1]]
#> IGRAPH 775bb4e UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 775bb4e (vertex names):
#> [1] a--b b--c a--j i--j
#>
#> [[2]]
#> IGRAPH 215172e UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 215172e (vertex names):
#> [1] a--b b--c c--d a--j
#>
#> [[3]]
#> IGRAPH e45f912 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from e45f912 (vertex names):
#> [1] a--b b--c c--d d--e
#>
# make_neighborhood_graph() is an alias of make_ego_graph()
make_neighborhood_graph(g, order = 2, 1:3)
#> [[1]]
#> IGRAPH 4497b6e UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 4497b6e (vertex names):
#> [1] a--b b--c a--j i--j
#>
#> [[2]]
#> IGRAPH 447ffd5 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 447ffd5 (vertex names):
#> [1] a--b b--c c--d a--j
#>
#> [[3]]
#> IGRAPH c49443d UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from c49443d (vertex names):
#> [1] a--b b--c c--d d--e
#>
# connecting to the neighborhood
g <- make_ring(10)
g <- connect(g, 2)
```