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In this work we make an attempt to understand social networks from a mathematical viewpoint. In the first instance we consider a network where each node representing an individual can connect with a neighbouring node with a certain…

We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers.…

We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…

Link prediction in complex networks has attracted considerable attention from interdisciplinary research communities, due to its ubiquitous applications in biological networks, social networks, transportation networks, telecommunication…

Many real-world networks exhibit degree-degree correlations between nodes separated by more than one step. Such long-range degree correlations (LRDCs) can be fully described by one joint and four conditional probability distributions with…

A longitudinal social network evolves over time through the creation and/ or deletion of links among a set of actors (e.g. individuals or organizations). Longitudinal social networks are studied by network science and social science…

Link prediction on dynamic networks has been extensively studied and widely applied in various applications. However, temporal unlink prediction, which also plays an important role in the evolution of social networks, has not been paid much…

Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…

Many network information theory problems face the similar difficulty of single letterization. We argue that this is due to the lack of a geometric structure on the space of probability distribution. In this paper, we develop such a…

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…

The problem of link prediction has attracted considerable recent attention from various domains such as sociology, anthropology, information science, and computer sciences. A link prediction algorithm is proposed based on link similarity…

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often non-Markovian, and the dynamics of their links correlated.…

Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks and social media. Having the knowledge…

Understanding how institutional changes within academia may affect the overall potential of science requires a better quantitative representation of how careers evolve over time. Since knowledge spillovers, cumulative advantage,…

Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…

An active line of research has used on-line data to study the ways in which discrete units of information---including messages, photos, product recommendations, group invitations---spread through social networks. There is relatively little…

We study the epidemic spreading on spatial networks where the probability that two nodes are connected decays with their distance as a power law. As the exponent of the distance dependence grows, model networks smoothly transition from the…

We consider the problem of predicting link formation in Social Learning Networks (SLN), a type of social network that forms when people learn from one another through structured interactions. While link prediction has been studied for…

Link prediction in complex networks--identifying the missing or future connections--remains a cornerstone problem for understanding network evolution and function, yet existing methods struggle to balance computational efficiency with…