Related papers: Local Clustering Coefficient in Generalized Prefer…
A prominent parameter in the context of network analysis, originally proposed by Watts and Strogatz (Collective dynamics of `small-world' networks, Nature 393 (1998) 440-442), is the clustering coefficient of a graph $G$. It is defined as…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Preferential attachment is a widely adopted paradigm for understanding the dynamics of social networks. Formal statistical inference,for instance GLM techniques, and model verification methods will require knowing test statistics are…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…
The global clustering coefficient is an effective measure for analyzing and comparing the structures of complex networks. The random annulus graph is a modified version of the well-known Erd\H{o}s-R\'{e}nyi random graph. It has been…
The clustering coefficient quantifies how well connected are the neighbors of a vertex in a graph. In real networks it decreases with the vertex degree, which has been taken as a signature of the network hierarchical structure. Here we show…
The Barab\'{a}si-Albert (BA) model is extended to include the concept of local world and the microscopic event of adding edges. With probability $p$, we add a new node with $m$ edges which preferentially link to the nodes presented in the…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…
The directed preferential attachment model is revisited. A new exact characterization of the limiting in- and out-degree distribution is given by two \emph{independent} pure birth processes that are observed at a common exponentially…
This paper presents a new definition of the community structure of a network, which takes also into account how communities are stratified. In particular, we extend the standard concept of clustering coefficient and provide the local…
In most networks, the connection between a pair of nodes is the result of their mutual affinity and attachment. In this letter, we will propose a Mutual Attraction Model to characterize weighted evolving networks. By introducing the initial…
In the study of ad hoc sensor networks, clustering plays an important role in energy conservation therefore analyzing the mechanics of such topology can be helpful to make logistic decisions .Using the theory of complex network the…
We present new results for LambdaCC and MotifCC, two recently introduced variants of the well-studied correlation clustering problem. Both variants are motivated by applications to network analysis and community detection, and have…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Practical analyses on the tail exponent of the power-law degree distribution use the Hill estimator as one…
We propose an extension of the preferential attachment scheme by allowing the connecting probability to depend on time t. We estimate the parameters involved in the model by minimizing the expected squared difference between the number of…
A network growth mechanism based on a two-step preferential rule is investigated as a model of network growth in which no global knowledge of the network is required. In the first filtering step a subset of fixed size $m$ of existing nodes…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
In this paper, we propose a novel statistic of networks, the normalized clustering coefficient, which is a modified version of the clustering coefficient that is robust to network size, network density and degree heterogeneity under…