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The study of networks has grown into a substantial interdisciplinary endeavour that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based…
Social norms and conventions are commonly accepted and adopted behaviors and practices within a social group that guide interactions -- e.g., how to spell a word or how to greet people -- and are central to a group's culture and identity.…
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
The robustness of complex networks was one of the first phenomena studied after the inception of network science. However, many contemporary presentations of this theory do not go beyond the original papers. Here we revisit this topic with…
Analyzing social networks is challenging. Key features of relational data require the use of non-standard statistical methods such as developing system-specific null, or reference, models that randomize one or more components of the…
Network models are widely used to represent relational information among interacting units and the structural implications of these relations. Recently, social network studies have focused a great deal of attention on random graph models of…
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the past decade, multilayer network science -- the branch of the field dealing with units interacting in multiple…
Basic principles of statistical inference are commonly violated in network data analysis. Under the current approach, it is often impossible to identify a model that accommodates known empirical behaviors, possesses crucial inferential…
There are two prominent paradigms to the modeling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Social network analysis is an important problem in data mining. A fundamental step for analyzing social networks is to encode network data into low-dimensional representations, i.e., network embeddings, so that the network topology…
Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction,…
Social Network Analysis is the use of Network and Graph Theory to study social phenomena, which was found to be highly relevant in areas like Criminology. This chapter provides an overview of key methods and tools that may be used for the…
Stochastic networks represent very important subject of research because they have been found in almost all branches of modern science, including also sociology and economy. We provide a information theory point of view, mostly based on its…
The aim of this article is to provide an understanding of social networks as a useful addition to the standard tool-box of techniques used by system designers. To this end, we give examples of how data about social links have been collected…
It is an increasingly common practice in several natural and social sciences to rely on network visualisations both as heuristic tools to get a first overview of relational datasets and as a way to offer an illustration of network analysis…