Finite-size Connectivity Phase Transitions in Blockchain Consensus Networks under Stochastic Degradation
Reji Kurien Thomas *
TOL Biotech, Kochi, India.
*Author to whom correspondence should be addressed.
Abstract
Blockchain consensus depends on distributed communication among nodes, and its liveness can be weakened when the underlying peer-to-peer overlay loses connectivity because of stochastic failures, node churn, routing disruption or adversarial degradation. This study develops a percolation-based framework for examining consensus feasibility in blockchain communication networks under stochastic connectivity loss. The communication layer is modelled using Erdős–Rényi random graph ensembles as a mathematically tractable synthetic baseline. Accordingly, the numerical results are interpreted as model-based connectivity thresholds for synthetic overlay ensembles, not as empirically measured thresholds for deployed blockchain networks. Link degradation is represented through bond percolation, where operational links are retained with probability q, giving an effective mean connectivity c_eff = qc. Consensus feasibility is evaluated using a simplified topology-level supermajority condition in which the giant connected component fraction satisfies S ≥ 2/3. This condition is treated as a necessary connectivity proxy for quorum-capable operation rather than as a protocol-specific guarantee of consensus. Analytical reasoning based on random graph connectivity and generating-function concepts is combined with Monte Carlo simulations to examine giant connected component emergence, finite-size threshold shifts, susceptibility behaviour and degradation under random and targeted link or node loss. The results show that quorum-capable connectivity requires stronger network conditions than ordinary giant-component emergence alone. Finite-size simulations indicate that the estimated consensus-connectivity threshold decreases with increasing network size, from approximately 0.92 for 500-node overlays to approximately 0.79 for 5000-node overlays. Networks with lower mean connectivity remain more vulnerable to probabilistic liveness collapse, particularly near the critical transition region. Targeted degradation of highly connected nodes produces faster fragmentation than random degradation, indicating that topology-aware attacks can substantially reduce consensus survivability in simplified overlay models. The proposed framework provides a topology-level method for relating network connectivity, link reliability and blockchain consensus feasibility under explicitly stated synthetic and stochastic assumptions.
Keywords: Blockchain consensus, percolation theory, finite-size scaling, stochastic degradation, peer-to-peer networks, giant connected component, Byzantine fault tolerance, network phase transitions, connectivity resilience, adversarial fragmentation