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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 5aa18d0:
#> [1] 1
#> 
#> [[2]]
#> + 1/10 vertex, from 5aa18d0:
#> [1] 2
#> 
#> [[3]]
#> + 1/10 vertex, from 5aa18d0:
#> [1] 3
#> 
ego(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 5aa18d0:
#> [1]  1  2 10
#> 
#> [[2]]
#> + 3/10 vertices, from 5aa18d0:
#> [1] 2 1 3
#> 
#> [[3]]
#> + 3/10 vertices, from 5aa18d0:
#> [1] 3 2 4
#> 
ego(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 5aa18d0:
#> [1]  1  2 10  3  9
#> 
#> [[2]]
#> + 5/10 vertices, from 5aa18d0:
#> [1]  2  1  3 10  4
#> 
#> [[3]]
#> + 5/10 vertices, from 5aa18d0:
#> [1] 3 2 4 1 5
#> 

# neighborhood() is an alias of ego()
neighborhood(g, order = 0, 1:3)
#> [[1]]
#> + 1/10 vertex, from 5aa18d0:
#> [1] 1
#> 
#> [[2]]
#> + 1/10 vertex, from 5aa18d0:
#> [1] 2
#> 
#> [[3]]
#> + 1/10 vertex, from 5aa18d0:
#> [1] 3
#> 
neighborhood(g, order = 1, 1:3)
#> [[1]]
#> + 3/10 vertices, from 5aa18d0:
#> [1]  1  2 10
#> 
#> [[2]]
#> + 3/10 vertices, from 5aa18d0:
#> [1] 2 1 3
#> 
#> [[3]]
#> + 3/10 vertices, from 5aa18d0:
#> [1] 3 2 4
#> 
neighborhood(g, order = 2, 1:3)
#> [[1]]
#> + 5/10 vertices, from 5aa18d0:
#> [1]  1  2 10  3  9
#> 
#> [[2]]
#> + 5/10 vertices, from 5aa18d0:
#> [1]  2  1  3 10  4
#> 
#> [[3]]
#> + 5/10 vertices, from 5aa18d0:
#> [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 edd6506 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from edd6506 (vertex names):
#> [1] a--b b--c a--j i--j
#> 
#> [[2]]
#> IGRAPH 48ad38c UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 48ad38c (vertex names):
#> [1] a--b b--c c--d a--j
#> 
#> [[3]]
#> IGRAPH 6ae4864 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 6ae4864 (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 33c5f8a UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 33c5f8a (vertex names):
#> [1] a--b b--c a--j i--j
#> 
#> [[2]]
#> IGRAPH 60de077 UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 60de077 (vertex names):
#> [1] a--b b--c c--d a--j
#> 
#> [[3]]
#> IGRAPH 195885b UN-- 5 4 -- Ring graph
#> + attr: name (g/c), mutual (g/l), circular (g/l), name (v/c)
#> + edges from 195885b (vertex names):
#> [1] a--b b--c c--d d--e
#> 

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