Contactability and Connectivity in Galactic Civilization Networks: A Network-Theoretic Framework for SETI

The probability of interstellar contact depends not only on the number of technological civilizations in the Galaxy but also on their ability to form communication networks. We investigate this problem using a network-theoretic approach in which civilizations are modeled as nodes randomly distributed within a Galactic disk and communication links are established whenever their separation is smaller than a characteristic communication distance. Monte Carlo simulations show that the network properties are governed by a single dimensionless parameter, η = N(cL/R)², where N is the number of civilizations, L is the communicative lifetime, c is the speed of light, and R is the Galactic radius. The probability of isolation follows P₀ ≃ e^(−η), and two characteristic thresholds are identified: a contact threshold at η_contact ≃ 1 and a network threshold at η_network ≃ 4.33, corresponding to the emergence of a giant connected component. These thresholds divide Galactic civilization networks into three connectivity regimes: the Isolation, Contact, and Network Phases. We further show that the framework can be combined with the Drake equation to derive quantitative conditions for interstellar contact. The results provide a network-theoretic framework for SETI and indicate that the absence of contact does not by itself require civilizations to be rare: insufficient Galactic connectivity, governed not by abundance alone but by the contactability parameter η, offers one possible interpretation of the Fermi paradox.