Adjacent
Definition
In graph theory, two vertices are adjacent if they are connected by an edge. Adjacent vertices can also be referred to as neighboring vertices.
5 Must Know Facts For Your Next Test
- Two vertices are considered adjacent if there is a direct edge connecting them.
- In an adjacency matrix, a '1' indicates that two vertices are adjacent, while a '0' means they are not.
- The degree of a vertex is the number of edges connected to it, which includes all adjacent vertices.
- An adjacency list for a graph represents each vertex and lists its adjacent vertices.
- Adjacency is fundamental in algorithms like Depth-First Search (DFS) and Breadth-First Search (BFS).
Review Questions
- What does it mean for two vertices to be adjacent in a graph?
- How is adjacency represented in an adjacency matrix?
- Why is understanding adjacency important for graph traversal algorithms?
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Related terms
vertex: A fundamental unit of which graphs are formed, representing nodes or points.
edge: A connection between two vertices in a graph.
adjacency matrix: A square matrix used to represent a finite graph, indicating which pairs of vertices are adjacent.
