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Author: Juan Carlos Bustamante
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Compute Environment: Ubuntu 18.04 (Deprecated)

Quelques exemples de graphes

typeset_mode(True)

Un graphe au hasard, faut spécifier le nombre de sommets et d'arêtes.


g = graphs.RandomGNM(10, 15)  # 10 sommets and 15 arêtes
show(g)
g.incidence_matrix()
d3-based renderer not yet implemented
[1 1 1 1 0 0 0 0 0 0 0 0 0 0 0] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 1 0 0 1 1 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 1 1 1 0 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 1 1 1 0] [0 0 0 0 1 0 0 0 0 0 0 1 0 0 1] [0 0 0 1 0 1 0 1 0 0 0 0 1 0 1] [0 0 0 0 0 0 0 0 1 1 0 0 0 1 0]

La chaîne de longueur nn

X = [[k, k+1] for k in range(4)]
g = Graph(X)
show(g)
d3-based renderer not yet implemented
G=Graph([["A","G"],["A","E"],["A","B"],["B","H"],["B","F"],["H","G"],["E","F"],["G","I"],["H","J"],["F","L"],["E","K"],["I","K"],["I","J"],["J","L"],["L","K"]])
G.show(layout="planar")


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%md
### La roue à $n+1$ sommets :
- $X=\{0,1,\ldots,n\}$
- $A = \{\{0,i\}| 1\leq i \leq n \} \cup \{ \{i,i+1\}| 1\leq i\leq n-1 \} \cup \{\{n,1\}\}$

La roue à n+1n+1 sommets :

  • X={0,1,…,n}X=\{0,1,\ldots,n\}
  • A={{0,i}∣1≤i≤n}∪{{i,i+1}∣1≤i≤n−1}∪{{n,1}}A = \{\{0,i\}| 1\leq i \leq n \} \cup \{ \{i,i+1\}| 1\leq i\leq n-1 \} \cup \{\{n,1\}\}
n=8
A1= [[0, k+1] for k in range(n)]
A2 = [[k, k+1] for k in range(1,n)]
A = A1+A2 + [[1,n]]
g=Graph(A)
show(g)
d3-based renderer not yet implemented

Les cubes

pour n≥1n\geq1 on définit le cube de dimension nn :

  • X={0,1}nX= \{0,1\}^n
  • A={{a1,…,an},{b1,…,bn}∣ai=bisauf pour exactement un indicei}A = \{\{a_1,\ldots,a_n\},\{b_1,\ldots,b_n\}| a_i = b_i \text{sauf pour exactement un indice} i \}
n=4
g=graphs.CubeGraph(n)
show(g)
d3-based renderer not yet implemented

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︠fdb9260f-46b0-460d-9d02-8d8cbbbe97b1i︠
%md
### Les graphes complets sur $n$ sommets.
On a $n$ sommets, et toutes les arêtes possibles.

Les graphes complets sur nn sommets.

On a nn sommets, et toutes les arêtes possibles.

K = graphs.CompleteGraph(21)
show(K)
d3-based renderer not yet implemented

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