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The ability to achieve coordinated behavior --engineered or emergent-- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the…

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…

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…

We consider two-opinion voter models on dense dynamic random graphs. Our goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion,…

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently…

The aim of this paper is to analyze a class of consensus algorithms with finite-time or fixed-time convergence for dynamic networks formed by agents with first-order dynamics. In particular, in the analyzed class a single evaluation of a…

We analyze access statistics of several popular webpages for a period of several years. The graphs of daily downloads are highly non-homogeneous with long periods of low activity interrupted by bursts of heavy traffic. These bursts are due…

The methods of non-homogeneous random graphs calibration are developed for social networks simulation. The graphs are calibrated by the degree distributions of the vertices and the edges. The mathematical foundation of the methods is formed…

Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…

The apparent disconnection between the microscopic and the macroscopic is a major issue in the understanding of complex systems. To this extend, we study the convergence of repeatedly applying local rules on a network, and touch on the…

Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…

Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…

Modern sociology has profoundly uncovered many convincing social criteria for behavioural analysis. Unfortunately, many of them are too subjective to be measured and presented in online social networks. On the other hand, data mining…

Social networks facilitate the social space where actors or the users have ties among them. The ties and their patterns are based on their life styles and communication. Similarly, in online social media networks like Facebook, Twitter,…

A continuous-opinion model accounting for the social compromise propensity is theoretically and numerically analysed. An agent's opinion is represented by a real number that can be changed through social interactions with her neighbours.…

An avalanche or cascade occurs when one event causes one or more subsequent events, which in turn may cause further events in a chain reaction. Avalanching dynamics are studied in many disciplines, with a recent focus on average avalanche…

Stream graphs are a very useful mode of representation for temporal network data, whose richness offers a wide range of possible approaches. The various methods aimed at generalising the classical approaches applied to static networks are…

Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…