Related papers: Clustering Properties of Spatial Preferential Atta…
Many complex networks from the World-Wide-Web to biological networks are growing taking into account the heterogeneous features of the nodes. The feature of a node might be a discrete quantity such as a classification of a URL document as…
We deal with a general preferential attachment graph model with multiple type edges. The types are chosen randomly, in a way that depends on the evolution of the graph. In the $N$-type case, we define the (generalized) degree of a given…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
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…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
Various models have been recently proposed to reflect and predict different properties of complex networks. However, the community structure, which is one of the most important properties, is not well studied and modeled. In this paper, we…
Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this…
In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…
We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
The scale-free model of Barabasi and Albert gave rise to a burst of activity in the field of complex networks. In this paper, we revisit one of the main assumptions of the model, the preferential attachment rule. We study a model in which…
In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
The evolution of random undirected graphs by the clustering attachment (CA) both without node and edge deletion and with uniform node or edge deletion is investigated. Theoretical results are obtained for the CA without node and edge…
We consider the preferential attachment model with location-based choice introduced by Haslegrave, Jordan and Yarrow as a model in which condensation phenomena can occur [Haslegrave et al. 2020]. In this model every vertex carries an…
We investigate a class of growing graphs embedded into the $d$-dimensional torus where new vertices arrive according to a Poisson process in time, are randomly placed in space and connect to existing vertices with a probability depending on…
Attributed graph clustering, which aims to group the nodes of an attributed graph into disjoint clusters, has made promising advancements in recent years. However, most existing methods face challenges when applied to large graphs due to…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
The phenomenon of six degrees of separation is an old but interesting problem. The considerations of the clustering coefficient reflecting triangular structures and its extension to square one to six degrees of separation have been…
Modern graph clustering applications require the analysis of large graphs and this can be computationally expensive. In this regard, local spectral graph clustering methods aim to identify well-connected clusters around a given "seed set"…