A node is a fundamental unit in graph theory that represents a distinct point or entity within a graph structure. As the basic building block of any graph, nodes serve as connection points that can be linked together through edges to represent relationships or connections. Each node can hold specific attributes, labels, or values that provide information about the entity it represents.
In practical applications, nodes can represent virtually any discrete entity or concept - from physical locations in a transportation network to users in a social media platform, or items in a recommendation system. The power of nodes lies in their ability to form complex networks through their connections, enabling the modeling of real-world systems and relationships. Nodes can be directed (having specific input and output connections) or undirected (having mutual connections), allowing for flexible representation of various types of relationships.
The properties of nodes within a graph can vary significantly based on their connections and position. Key characteristics include degree (number of connections), centrality (importance within the network), and reachability (which other nodes can be accessed from it). These properties make nodes essential for analyzing network structures, finding shortest paths, identifying important entities, and understanding the overall topology of the graph.
Common alternative names for nodes include:
The terms "node" and "vertex" are by far the most common and can be used interchangeably in most contexts, with "node" being more prevalent in computer science and applied fields, while "vertex" is more common in mathematical and theoretical contexts.
