This work presents a framework to analyze geometrical, topological and hydraulic properties of 3D Discrete Fracture Networks (DFN). A set of efficient algorithms have been developed to perform geometrical and topological analysis upon 3D networks of planar fractures with various shapes (mainly circular and ellipsoidal fractures). The present set of algorithms is capable of (i) calculating all possible intersections in the 3D networks and other geometrical attributes of the DFN; (ii) extracting the percolating clusters and eliminating dead end clusters; (iii) constructing the corresponding graph of the 3D network of planar fractures; and (iv) solving the 3D flow on the corresponding DFN graph (with impervious rock matrix). The innovations of the present approach concern mainly (a) the adaptation of the multiple labelling techniques for the search of clusters to the case of 3D DFN’s of planar fractures, and (b) the use of efficient algorithms to eliminate dead end clusters in DFN’s. The graph approach can be used to simulate the flow in the DFN by solving the Laplacian of the corresponding graph of the DFN (algebraic approach with rectangular matrices). This method enables, based on the detailed flow calculation, to obtain the upscaled permeability of the DFN in a computationally efficient way, which avoids the direct numerical simulation of flow on the DFN. Although the graph approach does not give exact equivalent permeability of the DFN, it enables a reliable estimation of the permeability while gaining several orders of magnitudes in terms of CPU time. Different options for the graph representation (nodes and links) are considered, with the nodes centered either on the planar fractures, or on the intersecting traces. Appropriate transmissivity measures between connected nodes are analyzed. Conclusions are drawn about the physical relevance of each approach, and their accuracy in estimating the equivalent permeability of the DFN.