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.

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Generating Random Networks and Graphs

10.1093/oso/9780198709893.001.0001 ◽

2017 ◽

Cited By ~ 8

Author(s):

Ton Coolen ◽

Alessia Annibale ◽

Ekaterina Roberts

Keyword(s):

Random Graph ◽

Random Graphs ◽

Scientific Method ◽

Preferential Attachment ◽

Worked Examples ◽

Configuration Model ◽

Random Networks ◽

Network Applications ◽

Starting Point ◽

Random Graph Generation

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.

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Renovating Watts and Strogatz Random Graph Generation by a Sequential Approach

Web Information Systems Engineering – WISE 2018 - Lecture Notes in Computer Science ◽

10.1007/978-3-030-02922-7_24 ◽

2018 ◽

pp. 348-363

Author(s):

Sadegh Nobari ◽

Qiang Qu ◽

Muhammad Muzammal ◽

Qingshan Jiang

Keyword(s):

Random Graph ◽

Sequential Approach ◽

Random Graph Generation ◽

Graph Generation

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The Impact of Edge Correlations in Random Networks

Complex Systems ◽

10.25088/complexsystems.30.4.525 ◽

2021 ◽

Vol 30 (4) ◽

pp. 525-537

Author(s):

András Faragó ◽

Keyword(s):

Random Graph ◽

Random Graphs ◽

Real Life ◽

Graph Model ◽

Random Networks ◽

Random Graph Model ◽

Special Cases ◽

Graph Parameters ◽

The Impact ◽

Good Number

Random graphs are frequently used models of real-life random networks. The classical Erdös–Rényi random graph model is very well explored and has numerous nontrivial properties. In particular, a good number of important graph parameters that are hard to compute in the deterministic case often become much easier in random graphs. However, a fundamental restriction in the Erdös–Rényi random graph is that the edges are required to be probabilistically independent. This is a severe restriction, which does not hold in most real-life networks. We consider more general random graphs in which the edges may be dependent. Specifically, two models are analyzed. The first one is called a p-robust random graph. It is defined by the requirement that each edge exist with probability at least p, no matter how we condition on the presence/absence of other edges. It is significantly more general than assuming independent edges existing with probability p, as exemplified via several special cases. The second model considers the case when the edges are positively correlated, which means that the edge probability is at least p for each edge, no matter how we condition on the presence of other edges (but absence is not considered). We prove some interesting, nontrivial properties about both models.

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