From 3b23eb2ac1dd9f99de70317f4313e33b4eb3ed4b Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Fri, 6 May 2022 17:38:59 +0200
Subject: [PATCH] added image and slide for adjacency

---
 slides/cours_24.md              | 100 ++++++++++++++++++++++++++++++++
 slides/figs/ex_graphe_cycle.pdf | Bin 0 -> 16261 bytes
 2 files changed, 100 insertions(+)
 create mode 100644 slides/figs/ex_graphe_cycle.pdf

diff --git a/slides/cours_24.md b/slides/cours_24.md
index 00061e1..28f05ba 100644
--- a/slides/cours_24.md
+++ b/slides/cours_24.md
@@ -244,5 +244,105 @@ avec $k$ la longueur de la chaîne (le nombre d'arêtes du chemin).
 
 :::
 
+# Généralités
+
+## Définition
+
+* Un graphe orienté est dit **fortement connexe**, s'il existe un chemin reliant n'importe quelle paire de sommets distincts.
+
+## Exemples
+
+\
+
+::: columns
+
+:::: column
+
+![Graphe fortement connexe.](figs/ex_graph_fort_connexe.pdf){width=60%}
+
+::::
+
+:::: column
+
+![Composantes fortement connexes. Source, Wikipédia: <https://bit.ly/3w5PL2l>](figs/composantes_fortement_connexes.svg){width=100%}
+
+::::
+
+:::
+
+# Généralités
+
+## Définition
+
+* Un **cycle** dans un graphe *non-orienté* est une chaîne de longueur $\leq 3$ telle que le 1er sommet de la chaîne est le même que le dernier, et dont les arêtes sont distinctes.
+* Pour un graphe *orienté* on parle de **circuit**.
+* Un graphe sans cycles est dit **acyclique**.
+
+## Exemples
+
+![Illustration de cycles, ou pas.](figs/ex_graphe_cycle.pdf){width=100%}
+
+# Question de la mort
+
+* Qu'est-ce qu'un graphe connexe acyclique?
+
+. . .
+
+* Un arbre!
+
+# Représentations
+
+* La complexité des algorithmes sur les graphes s'expriment en fonction du nombre de sommets $V$, et du nombre d'arêtes $E$:
+    * Si $|E|\sim |V|^2$, on dit que le graphe est **dense**.
+    * Si $|E|\sim |V|$, on dit que le graphe est **peu dense**.
+* Selon qu'on considère des graphes denses ou peu denses, différentes structure de données peuvent être envisagées.
+
+## Question
+
+* Comment peut-on représenter un graphe informatiquement? Des idées (réflexion de quelques minutes)?
+
+. . .
+
+* Matrice/liste d'adjacence.
+
+# Matrice d'adjacence
+
+* Soit le graphe $G(V,E)$, avec $V=\{1, 2, 3, ..., n\}$;
+* On peut représenter un graphe par une **matrice d'adjacence**, $A$, de dimension $n\times n$ définie par
+$$
+A_{ij}=\left\{ \begin{array}{ll}
+         1 & \mbox{si } i,j\in E,\\
+         0 & \mbox{sinon}.
+         \end{array} \right.
+$$
+
+
+::: columns
+
+:::: column
+
+## Exemple
+
+```{.mermaid format=pdf width=400 loc=figs/}
+graph LR;
+    1---2;
+    1---4;
+    2---5;
+    4---5;
+    5---3;
+```
+
+::::
+
+:::: column
+
+## Quelle est la matrice d'adjacence (1min)? 
+
+. . .
+
+::::
+
+:::
+
 
 
diff --git a/slides/figs/ex_graphe_cycle.pdf b/slides/figs/ex_graphe_cycle.pdf
new file mode 100644
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-- 
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