Adjazenzstruktur

Adjazenzstruktur refers to a data structure used in computer science to represent a graph. A graph consists of a set of vertices (nodes) and a set of edges connecting these vertices. The adjacency structure defines how these connections are stored and accessed. There are two primary forms of adjacency structures: adjacency matrices and adjacency lists.

An adjacency matrix is a square matrix where rows and columns represent vertices. A value of 1 (or true) at position (i, j) indicates an edge exists between vertex i and vertex j, while a 0 (or false) indicates no edge. For weighted graphs, the value can represent the weight of the edge. This structure is efficient for checking if an edge exists between two specific vertices, taking constant time. However, it can consume a significant amount of memory, especially for sparse graphs (graphs with few edges relative to the number of vertices), as it requires O(V^2) space, where V is the number of vertices.

An adjacency list, on the other hand, represents each vertex with a list of its adjacent vertices. For example, if vertex A is connected to vertices B and C, its adjacency list would contain B and C. This structure is more memory-efficient for sparse graphs, requiring O(V + E) space, where E is the number of edges. Iterating through all neighbors of a vertex is also efficient. However, checking for the existence of a specific edge can take time proportional to the number of neighbors of a vertex. The choice between an adjacency matrix and an adjacency list depends on the specific application and the characteristics of the graph being represented.