ExtendedConnectivity

ExtendedConnectivity is a term used in network science and graph theory to describe enhanced measures of a system's connectivity that extend beyond traditional static notions of connectedness. It typically incorporates additional dimensions such as time, multiple network layers, and reliability or redundancy.

In graphs, extended connectivity can refer to temporal connectivity, where links and nodes may appear or disappear over time, and to multiplex or multi-layer networks, where connections exist across different kinds of relations or modalities. In both cases, ExtendedConnectivity captures how robustly parts of the network remain reachable under changing conditions.

Computation of extended connectivity usually builds on standard algorithms for connectivity, flow, or path finding but must account for time and layer structure. This often involves temporal graphs, dynamic programming, or multi-criteria optimization, and may require approximations or heuristics for large-scale systems.

Applications are found in designing resilient communication and transportation networks, evaluating infrastructure vulnerability, epidemiological modeling on evolving contact networks, social network analysis, and cybersecurity planning.

The term is not standardized; different researchers define and measure ExtendedConnectivity in ways that suit specific contexts, leading to a family of related metrics rather than a single universal definition. It is the subject of ongoing study in fields concerned with robustness and adaptability of complex systems.

Related concepts include connectivity, temporal networks, multiplex networks, and resilience.