Saturation in Regular, Exotic and Random Pore Networks

Porcolation simulations were carried out on various networks: both regular and irregular. The saturation curve was obtained for cubic networks, localized and completely random 3D networks and networks based on exotic graphs like Sierpiński triangle and carpet. For the random graph generation, a modification of the cell list algorithm was introduced, which is capable of generating local random graphs efficiently. With the help of this graph generation method, the effect of locality was investigated, and it was proven to be an important property of random networks from the viewpoint of liquid propagation. The saturation curves of local random networks with different prescribed pore degree distributions were also obtained.

Generating Random Networks and Graphs

This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of random graph generation. This book is aimed at the graduate student or advanced undergraduate. It includes many worked examples, numerical simulations and exercises making it suitable for use in teaching. Explicit pseudocode algorithms are included to make the ideas easy to apply. Datasets are becoming increasingly large and network applications wider and more sophisticated. Testing hypotheses against properly specified control cases (null models) is at the heart of the ‘scientific method’. Knowledge on how to generate controlled and unbiased random graph ensembles is vital for anybody wishing to apply network science in their research.