This paper presents the Fuzzy Graph–Based Cryptographic Framework (FGCF), which couples continuous-valued membership functions from fuzzy graph theory with a discrete finite-field encryption core to yield a key generation engine whose entropy significantly exceeds that of binary-graph precursors. A fuzzy graph G̃ = (V, E, μ, ρ) is parameterized with Gaussian vertex memberships μ(v) ∈ [0,1] and edge memberships ρ(e) ≤ min(μ(u), μ(v)); its chromatic number, structural entropy, and fuzzy connectivity are jointly hashed into a 384-bit master key. Block encryption proceeds through modular multiplication over a prime field Zp, augmented by a depth-first search permutation layer that exploits the graph’s traversal ordering for diffusion. Testing on 10,000 randomized plaintext samples gives a Shannon entropy of 7.9999 bits/byte, an avalanche effect of 50.6±0.3%, a maximum differential probability of 2–6.2 and a key space of 2384. Throughput reaches 131 Mbps for 256-bit blocks on standard hardware and 47 Mbps on ARM Cortex-A72 at |V| = 8, confirming IoT viability.