Related papers: Clustering Properties of Spatial Preferential Atta…
We generalize the scale-free network model of Barab\`asi and Albert [Science 286, 509 (1999)] by proposing a class of stochastic models for scale-free interdependent networks in which interdependent nodes are not randomly connected but…
Social networks are organized into communities with dense internal connections, giving rise to high values of the clustering coefficient. In addition, these networks have been observed to be assortative, i.e. highly connected vertices tend…
Suppose in a graph $G$ vertices can be either red or blue. Let $k$ be odd. At each time step, each vertex $v$ in $G$ polls $k$ random neighbours and takes the majority colour. If it doesn't have $k$ neighbours, it simply polls all of them,…
In this work we study preference systems natural for the Peer-to-Peer paradigm. Most of them fall in three categories: global, symmetric and complementary. All these systems share an acyclicity property. As a consequence, they admit a…
Real-world social networks often exhibit high levels of clustering, positive degree assortativity, short average path lengths (small-world property) and right-skewed but rarely power law degree distributions. On the other hand homophily,…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…
We obtain the degree distribution for a class of growing network models on flat and curved spaces. These models evolve by preferential attachment weighted by a function of the distance between nodes. The degree distribution of these models…
We study an asymptotical behavior of the maximal degree in the degree distribution in an evolving tree model combining the local choice and the Mori's preferential attachment. In the considered model, the random graph is constructed in the…
Many complex systems in the real world can be characterized by attributed networks. To mine the potential information in these networks, deep embedded clustering, which obtains node representations and clusters simultaneously, has been paid…
The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…
Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…
Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…
The paper considers the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen (2018). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive…
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…
We consider a generalised d-dimensional model for asymptotically-scale-free geographical networks. Central to many networks of this kind, when considering their growth in time, is the attachment rule, i.e. the probability that a new node is…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
Graph-based clustering has shown promising performance in many tasks. A key step of graph-based approach is the similarity graph construction. In general, learning graph in kernel space can enhance clustering accuracy due to the…
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of…
We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected (``make friends with the friends of your…