In algorithmic terms, how is a graph defined?

A graph in algorithmic terms is defined as a structure composed of nodes (also known as vertices) and edges that represent connections or relationships between these nodes. This fundamental structure allows for the representation of various real-world problems, such as network topologies, social networks, or pathways in maps, where nodes can represent entities (like people or cities) and edges represent the relationships or paths between them.

Graphs can be directed or undirected, weighted or unweighted, providing versatility in how these relationships are modeled. The connections (edges) define how nodes are related to each other, enabling the analysis of complex networks and facilitating algorithms for traversal, shortest paths, or connectivity.

Understanding this definition is essential in computer science and algorithm design, as graphs form the backbone for many algorithms that solve practical problems in diverse fields such as computer networking, transportation logistics, and even social media analytics.