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Nodes and edges are fundamental concepts in graph theory, a branch of mathematics that studies the relationships between objects. A graph is a collection of nodes (also called vertices) and edges (also called links or arcs). Nodes represent entities, and edges represent the relationships or connections between these entities.

In a graph, nodes are typically denoted by circles or points, while edges are denoted by lines connecting these nodes. Edges can be directed or undirected. Directed edges, also known as arcs, have a direction, indicating a one-way relationship from one node to another. Undirected edges, on the other hand, do not have a direction, indicating a two-way relationship between nodes.

Graphs can be used to model a wide range of real-world systems and phenomena. For example, in a social network, nodes can represent individuals, and edges can represent friendships or interactions between them. In a computer network, nodes can represent devices, and edges can represent the connections between them.

Graphs can also be classified based on their properties. For example, a graph is said to be connected if there is a path between any two nodes. A graph is said to be acyclic if it does not contain any cycles, meaning there is no path that starts and ends at the same node. A graph is said to be weighted if each edge has an associated weight or cost, representing the strength or cost of the connection between nodes.