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Neighborhood of graph vertices

Source: R/games.R, R/structural-properties.R
ego.Rd

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. Negative values indicate an infinite order.

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.

connect_neighborhood(), vcount()

See also

Other functions for manipulating graph structure: +.igraph(), add_edges(), add_vertices(), complementer(), compose(), contract(), delete_edges(), delete_vertices(), difference(), difference.igraph(), disjoint_union(), edge(), igraph-minus, intersection(), intersection.igraph(), path(), permute(), rep.igraph(), reverse_edges(), simplify(), transitive_closure(), union(), union.igraph(), vertex()

Other structural.properties: bfs(), component_distribution(), constraint(), coreness(), degree(), dfs(), distance_table(), edge_density(), feedback_arc_set(), feedback_vertex_set(), girth(), is_acyclic(), is_dag(), is_matching(), k_shortest_paths(), knn(), 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 13c91ed:
#> [1] 1
#> 
#> [[2]]
#> + 1/10 vertex, from 13c91ed:
#> [1] 2
#> 
#> [[3]]
#> + 1/10 vertex, from 13c91ed:
#> [1] 3
#> 
ego(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 13c91ed:
#> [1]  1  2 10
#> 
#> [[2]]
#> + 3/10 vertices, from 13c91ed:
#> [1] 2 1 3
#> 
#> [[3]]
#> + 3/10 vertices, from 13c91ed:
#> [1] 3 2 4
#> 
ego(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 13c91ed:
#> [1]  1  2 10  3  9
#> 
#> [[2]]
#> + 5/10 vertices, from 13c91ed:
#> [1]  2  1  3 10  4
#> 
#> [[3]]
#> + 5/10 vertices, from 13c91ed:
#> [1] 3 2 4 1 5
#> 

# neighborhood() is an alias of ego()
neighborhood(g, order = 0, 1:3)
#> [[1]]
#> + 1/10 vertex, from 13c91ed:
#> [1] 1
#> 
#> [[2]]
#> + 1/10 vertex, from 13c91ed:
#> [1] 2
#> 
#> [[3]]
#> + 1/10 vertex, from 13c91ed:
#> [1] 3
#> 
neighborhood(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 13c91ed:
#> [1]  1  2 10
#> 
#> [[2]]
#> + 3/10 vertices, from 13c91ed:
#> [1] 2 1 3
#> 
#> [[3]]
#> + 3/10 vertices, from 13c91ed:
#> [1] 3 2 4
#> 
neighborhood(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 13c91ed:
#> [1]  1  2 10  3  9
#> 
#> [[2]]
#> + 5/10 vertices, from 13c91ed:
#> [1]  2  1  3 10  4
#> 
#> [[3]]
#> + 5/10 vertices, from 13c91ed:
#> [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 7c74b75 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 7c74b75 (vertex names):
#> [1] a--b b--c a--j i--j
#> 
#> [[2]]
#> IGRAPH ebb32ff UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from ebb32ff (vertex names):
#> [1] a--b b--c c--d a--j
#> 
#> [[3]]
#> IGRAPH 35a96f8 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 35a96f8 (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 6d58d4e UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 6d58d4e (vertex names):
#> [1] a--b b--c a--j i--j
#> 
#> [[2]]
#> IGRAPH 0882dd4 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 0882dd4 (vertex names):
#> [1] a--b b--c c--d a--j
#> 
#> [[3]]
#> IGRAPH a04efe9 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from a04efe9 (vertex names):
#> [1] a--b b--c c--d d--e
#> 

# connecting to the neighborhood
g <- make_ring(10)
g <- connect(g, 2)