Create an igraph graph from a list of edges, or a notable graph

## Arguments

- edges
A vector defining the edges, the first edge points from the first element to the second, the second edge from the third to the fourth, etc. For a numeric vector, these are interpreted as internal vertex ids. For character vectors, they are interpreted as vertex names.

Alternatively, this can be a character scalar, the name of a notable graph. See Notable graphs below. The name is case insensitive.

Starting from igraph 0.8.0, you can also include literals here, via igraph's formula notation (see

`graph_from_literal()`

). In this case, the first term of the formula has to start with a ‘`~`

’ character, just like regular formulae in R. See examples below.- ...
For

`make_graph()`

: extra arguments for the case when the graph is given via a literal, see`graph_from_literal()`

. For`directed_graph()`

and`undirected_graph()`

: Passed to`make_directed_graph()`

or`make_undirected_graph()`

.- n
The number of vertices in the graph. This argument is ignored (with a warning) if

`edges`

are symbolic vertex names. It is also ignored if there is a bigger vertex id in`edges`

. This means that for this function it is safe to supply zero here if the vertex with the largest id is not an isolate.- isolates
Character vector, names of isolate vertices, for symbolic edge lists. It is ignored for numeric edge lists.

- directed
Whether to create a directed graph.

- dir
It is the same as

`directed`

, for compatibility. Do not give both of them.- simplify
For graph literals, whether to simplify the graph.

## Notable graphs

`make_graph()`

can create some notable graphs. The name of the
graph (case insensitive), a character scalar must be supplied as
the `edges`

argument, and other arguments are ignored. (A warning
is given is they are specified.)

`make_graph()`

knows the following graphs:

- Bull
The bull graph, 5 vertices, 5 edges, resembles to the head of a bull if drawn properly.

- Chvatal
This is the smallest triangle-free graph that is both 4-chromatic and 4-regular. According to the Grunbaum conjecture there exists an m-regular, m-chromatic graph with n vertices for every m>1 and n>2. The Chvatal graph is an example for m=4 and n=12. It has 24 edges.

- Coxeter
A non-Hamiltonian cubic symmetric graph with 28 vertices and 42 edges.

- Cubical
The Platonic graph of the cube. A convex regular polyhedron with 8 vertices and 12 edges.

- Diamond
A graph with 4 vertices and 5 edges, resembles to a schematic diamond if drawn properly.

- Dodecahedral, Dodecahedron
Another Platonic solid with 20 vertices and 30 edges.

- Folkman
The semisymmetric graph with minimum number of vertices, 20 and 40 edges. A semisymmetric graph is regular, edge transitive and not vertex transitive.

- Franklin
This is a graph whose embedding to the Klein bottle can be colored with six colors, it is a counterexample to the necessity of the Heawood conjecture on a Klein bottle. It has 12 vertices and 18 edges.

- Frucht
The Frucht Graph is the smallest cubical graph whose automorphism group consists only of the identity element. It has 12 vertices and 18 edges.

- Grotzsch
The Groetzsch graph is a triangle-free graph with 11 vertices, 20 edges, and chromatic number 4. It is named after German mathematician Herbert Groetzsch, and its existence demonstrates that the assumption of planarity is necessary in Groetzsch's theorem that every triangle-free planar graph is 3-colorable.

- Heawood
The Heawood graph is an undirected graph with 14 vertices and 21 edges. The graph is cubic, and all cycles in the graph have six or more edges. Every smaller cubic graph has shorter cycles, so this graph is the 6-cage, the smallest cubic graph of girth 6.

- Herschel
The Herschel graph is the smallest nonhamiltonian polyhedral graph. It is the unique such graph on 11 nodes, and has 18 edges.

- House
The house graph is a 5-vertex, 6-edge graph, the schematic draw of a house if drawn properly, basicly a triangle of the top of a square.

- HouseX
The same as the house graph with an X in the square. 5 vertices and 8 edges.

- Icosahedral, Icosahedron
A Platonic solid with 12 vertices and 30 edges.

- Krackhardt kite
A social network with 10 vertices and 18 edges. Krackhardt, D. Assessing the Political Landscape: Structure, Cognition, and Power in Organizations. Admin. Sci. Quart. 35, 342-369, 1990.

- Levi
The graph is a 4-arc transitive cubic graph, it has 30 vertices and 45 edges.

- McGee
The McGee graph is the unique 3-regular 7-cage graph, it has 24 vertices and 36 edges.

- Meredith
The Meredith graph is a quartic graph on 70 nodes and 140 edges that is a counterexample to the conjecture that every 4-regular 4-connected graph is Hamiltonian.

- Noperfectmatching
A connected graph with 16 vertices and 27 edges containing no perfect matching. A matching in a graph is a set of pairwise non-adjacent edges; that is, no two edges share a common vertex. A perfect matching is a matching which covers all vertices of the graph.

- Nonline
A graph whose connected components are the 9 graphs whose presence as a vertex-induced subgraph in a graph makes a nonline graph. It has 50 vertices and 72 edges.

- Octahedral, Octahedron
Platonic solid with 6 vertices and 12 edges.

- Petersen
A 3-regular graph with 10 vertices and 15 edges. It is the smallest hypohamiltonian graph, i.e. it is non-hamiltonian but removing any single vertex from it makes it Hamiltonian.

- Robertson
The unique (4,5)-cage graph, i.e. a 4-regular graph of girth 5. It has 19 vertices and 38 edges.

- Smallestcyclicgroup
A smallest nontrivial graph whose automorphism group is cyclic. It has 9 vertices and 15 edges.

- Tetrahedral, Tetrahedron
Platonic solid with 4 vertices and 6 edges.

- Thomassen
The smallest hypotraceable graph, on 34 vertices and 52 edges. A hypotraceable graph does not contain a Hamiltonian path but after removing any single vertex from it the remainder always contains a Hamiltonian path. A graph containing a Hamiltonian path is called traceable.

- Tutte
Tait's Hamiltonian graph conjecture states that every 3-connected 3-regular planar graph is Hamiltonian. This graph is a counterexample. It has 46 vertices and 69 edges.

- Uniquely3colorable
Returns a 12-vertex, triangle-free graph with chromatic number 3 that is uniquely 3-colorable.

- Walther
An identity graph with 25 vertices and 31 edges. An identity graph has a single graph automorphism, the trivial one.

- Zachary
Social network of friendships between 34 members of a karate club at a US university in the 1970s. See W. W. Zachary, An information flow model for conflict and fission in small groups, Journal of Anthropological Research 33, 452-473 (1977).

## See also

Other deterministic constructors:
`graph_from_atlas()`

,
`graph_from_edgelist()`

,
`graph_from_literal()`

,
`make_chordal_ring()`

,
`make_empty_graph()`

,
`make_full_citation_graph()`

,
`make_full_graph()`

,
`make_lattice()`

,
`make_ring()`

,
`make_star()`

,
`make_tree()`

## Examples

```
make_graph(c(1, 2, 2, 3, 3, 4, 5, 6), directed = FALSE)
#> IGRAPH 7a324aa U--- 6 4 --
#> + edges from 7a324aa:
#> [1] 1--2 2--3 3--4 5--6
make_graph(c("A", "B", "B", "C", "C", "D"), directed = FALSE)
#> IGRAPH 69576dd UN-- 4 3 --
#> + attr: name (v/c)
#> + edges from 69576dd (vertex names):
#> [1] A--B B--C C--D
solids <- list(
make_graph("Tetrahedron"),
make_graph("Cubical"),
make_graph("Octahedron"),
make_graph("Dodecahedron"),
make_graph("Icosahedron")
)
graph <- make_graph(
~ A - B - C - D - A, E - A:B:C:D,
F - G - H - I - F, J - F:G:H:I,
K - L - M - N - K, O - K:L:M:N,
P - Q - R - S - P, T - P:Q:R:S,
B - F, E - J, C - I, L - T, O - T, M - S,
C - P, C - L, I - L, I - P
)
```