4adjacency

4adjacency refers to a concept in graph theory that describes a specific type of relationship between vertices in a graph. In a graph, vertices are nodes, and edges are the connections between them. When we talk about adjacency, we are concerned with which vertices are directly connected to each other.

The term "4adjacency" implies a measure of how "close" or "connected" vertices are, extending beyond immediate neighbors. While standard adjacency typically means vertices are connected by a single edge, 4adjacency suggests a connection that is at most four edges away. This means that two vertices are considered 4adjacent if there is a path of length 1, 2, 3, or 4 between them.

This concept is useful in analyzing network structures where direct connections might be less important than the ability to reach a node within a few steps. For example, in social networks, 4adjacency could represent people you can reach through a small number of intermediaries, indicating a relatively close social circle. In telecommunications networks, it might indicate how quickly information can be routed between nodes. The precise definition and application of 4adjacency would depend on the specific context and the type of graph being analyzed. It is a way to group or classify vertices based on their reachability within a defined limit.