A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering conditional probabilities that two randomly chosen vertices are adjacent given that they have r common neighbours. We denote such probabilities cl(r) and call r ...

We proposed a deterministic multidimensional growth model for small-world networks. The model can characterize the distinguishing properties of many real-life networks with geometric space structure. Our results show the model possesses small-world effect: larger clustering coefficient and smaller characteristic path length. We also obtain some accurate results for its properties including degr...

Generalized Farey tree network (GFTN) model with small-world is proposed, and the topological characteristics are studied by both theoretical analysis and numerical simulations, which are in good accordance with each other. Analytical results show that the degree distribution of the GFTN is exponential. As the number of network nodes increasing with time interval (or level number), t, the clust...

Dynamic random network models are presented as a mathematical framework for modelling and analyzing the time evolution of complex networks. Such framework allows the time analysis of several network characterizing features such as link density, clustering coefficient, degree distribution, as well as entropy-based complexity measures, providing new insight on the evolution of random networks. So...

Choosing a subgraph that can concisely represent a large real-world graph is useful in many scenarios. The usual strategy employed is to sample nodes so that the induced subgraph matches the original graph’s degree distribution, clustering coefficient, etc., but no attempt is made to preserve fine-grained relationships between nodes, which are vital for applications like clustering, classificat...

Complex networks which describe biological systems such as gene regulations and metabolisms indicate several striking statistical properties such as power-law degree distribution P (k)∼k−γ that is a scalefree property and high clustering coefficient, yielding nontrivial interpretations for topologies and signal transductions of the networks [1]. In this report, we forcus on degree correlation k̄...

In this paper, we study the clustering properties of the Spatial Preferential Attachment (SPA) model introduced by Aiello et al. in 2009. This model naturally combines geometry and preferential attachment using the notion of spheres of influence. It was previously shown in several research papers that graphs generated by the SPA model are similar to real-world networks in many aspects. For exam...

Soil nitrate-nitrogen (NO3-N) data arranged on a three-dimensional grid were analyzed to compare tillage effect on the spatial distribution of residual NO3-N in the soil profile of agricultural plots drained by subsurface tiles. A three-dimensional median-based resistant (to outlier(s)) approach was developed to polish the spatially located data on soil NO3-N affected by directional trends (non...

Experimental results show that in large complex networks (such as internet, social or biological networks) there exists a tendency to connect elements which have a common neighbor. In theoretical random graph models, this tendency is described by the clustering coefficient being bounded away from zero. Complex networks also have power-law degree distributions and short average distances (small ...

Spearman’s rank correlation coefficient is a nonparametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of an association between two variables. It is a measure of a monotone association that is used when the distribution of data makes Pearson’s correlation coefficient undesirable or misleading. Spearman’s coefficient is not a measure of the linea...