In computer science and discrete mathematics, graph representation defines the structural mapping of abstract entities (vertices) and their relationships (edges) into computational data structures known primarily as adjacency matrices or linked lists. This concept establishes the formal correspondence between a set theoretic relation \(R \subseteq V \times V\) over a vertex set \(V\) and its two primary algebraic encodings: symmetric tensor representations for dense connectivity via Boolean/weighted arrays, and sparse chain-reaction pointers in list-based structures that optimize space complexity relative to edge count. These theoretical constructs serve as the foundational interface for traversability analysis within graph theory, enabling efficient computational access properties required by subsequent algorithms dependent on weight aggregation and path enumeration mechanics.
Adjacency matrix representation stores a graph's edges in a V×V two-dimensional array indexed by vertex indices, where cell [i][j] holds a boolean (or, for weighted graphs, the edge weight with a sen…