Faults are essential subsurface features affecting the mechanical and hydraulic properties of rock masses. However, interpreting faults from seismic images may lead to various scenarios reflecting the uncertainty due to the seismic image quality and fault zone definition. Actually, some details of the fault network may be invisible because of the seismic image resolution. For instance, one large fault can be seen as a single feature or as a collection of smaller ones and the uncertainty on the connectivity of such small features may be under-estimated. The goal of this work is to quantify the uncertainty related to the number and connectivity of faults honoring a likelihood image, built from seismic image. A marked point process framework is adopted to capture the geometry and the topology of fault network while using a data conditioning strategy to account for fault localization. This modeling strategy enables a construction of a Gibbs probability distribution to characterize fault networks. The output realizations are sampled from this distribution using the Metropolis-Hastings algorithm. To characterize these realizations, the visit map is constructed to visualize regions of highest posterior probabilities of fault presence. The approach is applied on the Volve data, acquired in the Central North Sea.