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Many empirical networks display an inherent tendency to cluster, i.e. to form circles of connected nodes. This feature is typically measured by the clustering coefficient (CC). The CC, originally introduced for binary, undirected graphs,…
With the increasing availability of behavioral data from diverse digital sources, such as social media sites and cell phones, it is now possible to obtain detailed information about the structure, strength, and directionality of social…
We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…
Social networks have been widely studied over the last century from multiple disciplines to understand societal issues such as inequality in employment rates, managerial performance, and epidemic spread. Today, these and many more issues…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
Power law distribution is common in real-world networks including online social networks. Many studies on complex networks focus on the characteristics of vertices, which are always proved to follow the power law. However, few researches…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
It has often been taken as a working assumption that directed links in information networks are frequently formed by "short-cutting" a two-step path between the source and the destination -- a kind of implicit "link copying" analogous to…
Graph drawings are useful tools for exploring the structure and dynamics of data that can be represented by pair-wise relationships among a set of objects. Typical real-world social, biological or technological networks exhibit high…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
Understanding real-world networks has been a core research endeavor throughout the last two decades. Network Creation Games are a promising approach for this from a game-theoretic perspective. In these games, selfish agents corresponding to…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
Degree distributions are arguably the most important property of real world networks. The classic edge configuration model or Chung-Lu model can generate an undirected graph with any desired degree distribution. This serves as a good null…
The line graphs are clustered and assortative. They share these topological features with some social networks. We argue that this similarity reveals the cliquey character of the social networks. In the model proposed here, a social network…