What does "adjacency" of vertices in a graph mean?

Adjacency of vertices means that two vertices are connected by an edge.

If there is an edge between vertices A and B, then:

• In an undirected graph - A and B are adjacent (A ↔ B).
• In a directed graph - • if there is an edge A → B, then B is adjacent to A in the direction from A to B, • but not necessarily the other way around.

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Examples:

• In a social network: if two users are "friends", their vertices are adjacent.
• On a route: if there is a road between cities, the cities are adjacent.

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Adjacent vertices are often stored in an adjacency list - each vertex has a record of all the vertices it is connected to.

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Summary: adjacency is a sign of a direct connection: vertices are considered adjacent if there is an edge between them.