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. Rock fractures organize as networks, exhibiting natural variation in theirspatial arrangements. Therefore, identifying, quantifying, and comparingvariations in spatial arrangements within network geometries are of interestwhen explicit fracture representations or discrete fracture network models arechosen to capture the influence of fractures on bulk rock behaviour. Treatingfracture networks as spatial graphs, we introduce a novel approach to quantifyspatial variation. The method combines graph similarity measures withhierarchical clustering and is applied to investigate the spatial variationwithin large-scale 2-D fracture networks digitized from the well-known Lilstocklimestone pavements, Bristol Channel, UK. We consider three large, fracturedregions, comprising nearly 300 000 fractures spread over14 200 m2 from the Lilstock pavements.Using a moving-window sampling approach, we first subsample the large networksinto subgraphs. Four graph similarity measures – fingerprint distance, D-measure,Network Laplacian spectral descriptor (NetLSD), and portraitdivergence – that encapsulate topological relationships and geometry of fracturenetworks are then used to compute pair-wise subgraph distances serving as inputfor the statistical hierarchical clustering technique. In the form of hierarchicaldendrograms and derived spatial variation maps, the results indicate spatialautocorrelation with localized spatial clusters that gradually vary overdistances of tens of metres with visually discernable and quantifiable boundaries.Fractures within the identified clusters exhibit differences in fractureorientations and topology. The comparison of graph similarity-derivedclusters with fracture persistence measures indicates an intra-networkspatial variation that is not immediately obvious from the ubiquitous fractureintensity and density maps. The proposed method provides a quantitative way toidentify spatial variations in fracture networks, guiding stochastic andgeostatistical approaches to fracture network modelling.

Investigating spatial heterogeneity within fracture networks using hierarchical clustering and graph distance metrics