Gaussian Disorder Effects in Bravais Lattices

Real-world materials and complex systems often exhibit varying degrees of structural disorder, which profoundly affects their physical properties and embedded dynamical processes. We present a characterization of three distinct Bravais lattice types — primitive orthorhombic, tetragonal, and hexagonal — subjected to Gaussian displacements of node positions, which models the topological disorder inherent in physical realizations. Random displacements of network nodes are controlled by a normalized standard deviation parameter s. Using the connection principles of the Relative Neighborhood Graph (RNG) and the Gabriel Graph (GG), we generate disordered networks that continuously interpolate between crystalline order at s = 0 and total spatial randomness at s = 1. We carry out a topological analysis of the selected lattices, each chosen to exemplify different symmetries and coordination geometries. We quantify how network structures evolve with the parameter s by computing key network properties, including average connectivity, degree distribution, clustering coefficient, average path length, and network diameter. Comparative results reveal how the underlying lattice structure and the Gaussian noise parameter jointly determine the emergent network topology, offering a framework for studying disorder and connectivity in spatially embedded systems. Our results highlight how structural disorder shapes connectivity in real materials and spatial networks, bridging idealized lattice models with the complex architectures observed in nature and technology.