👉 Nodes in mathematics, particularly within graph theory and discrete mathematics, are fundamental building blocks that represent points or vertices in a structure known as a graph. Each node can have one or more edges connecting it to other nodes, forming a network of interconnected points. These connections can be directed (indicating a one-way relationship) or undirected (indicating a two-way relationship). The nodes can also have associated values or attributes, such as weights in weighted graphs, which quantify the strength or cost of connections between nodes. Nodes serve as the core elements in analyzing and understanding graph properties, such as connectivity, paths, cycles, and centrality measures, which are crucial in various applications including network analysis, social network modeling, and optimization problems.
