Related papers: Closure coefficients in scale-free complex network…
We present a new network model accounting for multidimensional assortativity. Each node is characterized by a number of features and the probability of a link between two nodes depends on common features. We do not fix a priori the total…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
Clustering network is one of which complex network attracting plenty of scholars to discuss and study the structures and cascading process. We primarily analyzed the effect of clustering coefficient to other various of the single clustering…
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces.…
The random networks enriched with additional structures as metric and group-symmetry in background metric space are investigated. The important quantities like he clustering coefficient as well as the mean degree of separation in such…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
We investigate the higher-order connectivity of scale-free networks using algebraic topology. We model scale-free networks as preferential attachment graphs, and we study the algebraic-topological properties of their clique complexes. We…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…
A widely-used operation on graphs is local clustering, i.e., extracting a well-characterized community around a seed node without the need to process the whole graph. Recently local motif clustering has been proposed: it looks for a local…
The (variational) graph auto-encoder and its variants have been popularly used for representation learning on graph-structured data. While the encoder is often a powerful graph convolutional network, the decoder reconstructs the graph…
Triangle-free graphs play a central role in graph theory, and triangle detection (or triangle finding) as well as triangle enumeration (triangle listing) play central roles in the field of graph algorithms. In distributed computing,…
Triangles are abundant in real-world networks but rare in standard null models for sparse graphs. Existing explanations typically rely on explicit triadic closure mechanisms or geometry-based connection rules. We propose an alternative…
Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…
We study the influence of clustering, more specifically triangles, on cascading failures in interdependent networks or systems, in which we model the dependence between comprising systems using a dependence graph. First, we propose a new…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
Many real systems exhibit the processes of growth and shrink. In this paper, we propose a network evolution model based on the simultaneous application of both node addition and deletion rules. To obtain a higher clustering that is present…
The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…
We establish asymptotic vertex degree distribution and examine its relation to the clustering coefficient in two popular random intersection graph models of Godehardt and Jaworski [Electron. Notes Discrete Math. 10 (2001) 129-132]. For…
Node copying is an important mechanism for network formation, yet most models assume uniform copying rules. Motivated by observations of heterogeneous triadic closure in real networks, we introduce the concept of a hidden network model - a…