Graphs ¶

Graphs are a data structures which represent a set of nodes and edges connecting them. They are used to represent relationships between objects. Graphs are used in many fields, such as social networks, transportation networks, and computer networks.

Undirected Graphs¶

Undirected graphs are graphs where the edges do not have a direction. This means that if there is an edge between two nodes, then there is also an edge between those nodes in the opposite direction.

graph LR
    A((Node A)) --- B((Node B))
    A --- C((Node C))
    A --- D((Node D))
    C --- D

Directed Graphs¶

Directed graphs are graphs where the edges have a direction. This means that if there is an edge between two nodes, then there is not necessarily an edge between those nodes in the opposite direction.

graph LR
    A((Node A)) --> B((Node B))
    A --> C((Node C))
    B --> C
    C --> D((Node D))
    D --> A

Weighted Graphs¶

Weighted graphs are graphs where the edges have a weight. This means that each edge has a value associated with it. This value can be used to represent the cost of traversing the edge.

graph LR
    A((A))---|2|B((B));
    A-->|5|C((C));
    B-->|1|C;
    B---|3|D((D));
    C-->|4|D;

Binary Trees¶

Binary trees are a type of tree where each node has at most two children. These children are referred to as the left child and the right child.

graph TD
    A((A))---B((B));
    A-->C((C));
    B-->D((D));
    B---E((E));
    C-->F((F));