A descriptive study of fracture networks in rocks using complex network metrics

• Topological characterization of fracture networks in rocks by centrality measures.
• Communicability measures for characterizing fractures systems in rocks.
• Identification of a topological class for fractures networks.

In this paper we describe the static topological fracture structure of five rock samples from three regions in Eastern Mexico by the application of centrality and communicability measures used in the area of complex networks. The information obtained from fracture images is used to characterize the fracture networks. The analysis is divided into two groups of characteristics. The first provides a general summary of the fracture network through the description of the number of nodes, edges, diameter, radius, lengths and clustering coefficients. A second group of features centers on the description of communicability in the network by means of three indexes recently proposed. In addition, we apply centrality measures (betweenness, closeness, eigenvector and eccentricity) for quantifying the importance of nodes in the entire network. Finally, we identify a topology for fracture networks using a classification based on the degree of communicability. The most important results obtained in this work are focused in the topological characteristic patterns found in fracture networks applying the approach of complex networks that in general provide local and global parameters of connectivity and communicability.