The increasing use of the Blockchain systems in industries such as finance, supply chains and even smart cities has increased the need for robust and scalable security mechanisms. Although existing blockchain security approaches primarily focus on cryptographic techniques and consensus algorithms, they do not take the geometry of the network produced by the underlying peer-to-peer network, and are vulnerable to connectivity-based attacks like partitioning attacks, Sybil attacks and eclipse attacks. This weakness shows the necessity to have topology aware security architecture that can make the network more resilient and efficient. The paper proposes a security model to graphically represent blockchain networks as graphs and uses graph-theoretic measures to quantify vulnerabilities and optimize networks. It seeks to optimize network performance, strength and resilience to faults through incorporation of trust-conscious node evaluation and dominating set optimization. A graph representation, G (V,E) is constructed, connectivity measures (vertex, edge connectivity, centrality and clustering coefficient) are computed and a secure node selection algorithm is developed to enable connectivity-preserving routing. The experimental evaluation compares the proposed framework with baseline and conventional secure routing approaches using network resilience, transaction propagation delay, and clustering coefficient as performance metrics. The results indicate improvements in network resilience under simulated attack conditions, reduced transaction propagation time, and increased clustering coefficients, suggesting enhanced local connectivity and network redundancy.