Unreachability

Unreachability refers to the condition in which a target cannot be reached from a given source. It is used in mathematics, computer science, networking, and everyday language to describe the absence of a path, route, contact, or information flow between two points or states.

In graph theory and computing, reachability is the existence of a path from one node to another following the direction of edges. If no such path exists, the target is unreachable from the source. This concept underpins algorithms for searching and navigation, such as breadth-first search and depth-first search, and for computing transitive closure. Unreachability is central to notions of connectivity and to the study of strongly connected components in directed graphs.

In communications and networking, unreachability often signals a partition or a failure in the network, where messages cannot be delivered to a destination. Causes can include link outages, routing misconfigurations, or policy filters. Operators use tests like ping and traceroute, and routing protocols aim to maintain reachability through redundancy and dynamic path selection.

In practical terms, unreachability informs reliability assessments, access control, and geographic or social models where certain targets are permanently or temporarily inaccessible. It is distinguished from nonexistence, where a target does not exist rather than being unavailable. See also reachability and connectivity.