<b>A modified node-based measure for estimating the connectedness of fracture patterns</b>

Connectivity is a key factor governing the permeability and flow behavior of fracture networks. Topological graph theory has recently been applied to quantify connectivity, where topological connectivity (C_L) is defined by the relative proportions of ‘X’, ‘Y’, and ‘I’ nodes—representing cross-cutting, abutting, and isolated nodes, respectively—without accounting for their spatial distribution. As a result, fracture maps with very different spatial arrangements may yield the same C_L values, making this parameter inadequate for predicting percolation properties. To overcome this limitation, we propose a modified parameter, <i>S-connectivity (Sc)</i>, which integrates both node abundance and spatial distribution. Spatial distribution is captured using the statistical measure <i>lacunarity</i>. S_c is defined as the product of C_L and a weighting factor (κ), where κ is derived from the normalized lacunarity of the combined ‘X’ and ‘Y’ nodes (termed ‘XY’-nodes).We evaluated S_c using synthetic fracture maps with identical C_L values but different node distributions. S_c successfully distinguished between these maps. Numerical flow simulations further demonstrated that S_c correlates positively with equivalent permeability, providing better predictive accuracy than C_L alone. Analysis of natural fracture patterns from a fault damage zone confirmed the consistent positive relationship between S_c and equivalent permeability. These findings highlight <i>S-connectivity</i> as a more robust and distinctive measure of fracture network connectivity, offering valuable applications for modeling and engineering tasks in fractured petroleum reservoirs and aquifers.