Related papers: Inter-layer Degree Correlations in Heterogeneously…
Community structures in collaboration networks reflect the natural tendency of individuals to organize their work in groups in order to better achieve common goals. In most of the cases, individuals exploit their connections to introduce…
Introduced recently, the concept of hierarchical degree allows a more complete characterization of the topological context of a node in a complex network than the traditional node degree. This article presents analytical characterization…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
Since their inception about a decade ago, dynamic networks which adapt to the state of the nodes have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically…
Models of growing networks are a central topic in network science. In these models, vertices are usually labeled by their arrival time, distinguishing even those node pairs whose structural roles are identical. In contrast, unlabeled…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
The parallel computational complexity or depth of growing network models is investigated. The networks considered are generated by preferential attachment rules where the probability of attaching a new node to an existing node is given by a…
The way the topological structure goes from a decoupled state into a coupled one in multiplex networks has been widely studied by means of analytical and numerical studies, involving models of artificial networks. In general, these…
A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population…
Preferential attachment, homophily and, their consequences such as the glass ceiling effect have been well-studied in the context of undirected networks. However, the lack of an intuitive, theoretically tractable model of a directed,…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity…
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…
Real networks often have severe degree heterogeneity, with the maximum, average, and minimum node degrees differing significantly. This paper examines the impact of degree heterogeneity on statistical limits of network data analysis.…
We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree…
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
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…