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 of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Given a snapshot of a social network, can we infer which new interactions among its members are likely to occur in the near future? We formalize this question as the link-prediction problem, and we develop approaches to link prediction based on measures for analyzing the “proximity” of nodes in a network. Experiments on large co-authorship networks suggest that information about future interactions can be extracted from network topology alone, and that fairly subtle measures for detecting node proximity can outperform more direct measures. 1

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 artificial networks of such a kind came into existence recently. This opens a wide field for the study of their topology, evolution, and complex processes occurring in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of large sizes of these networks, the distances between most their vertices are short — a feature known as the “smallworld” effect. We discuss how growing networks self-organize into scale-free structures and the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation in these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in Nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems

Abstract — Social networking services are a fast-growing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in real-life social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld’s ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data’s degree distribution exhibits a multi-scaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two exponents corresponds to the different segments in Cyworld’s degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from close-knit online social networks which show a similar degree correlation pattern to real-life social networks. I.

Many systems take the form of networks, including the Internet, distribution and transport networks, neural networks, food webs, and social networks. The characterization and modelling of these systems has proved amenable to treatment using techniques drawn from statistical and computational physics, and has as a result attracted considerable attention in the physics literature in recent years. In this paper the author reviews some of the interesting issues in this area and recounts some recent work on these issues by his group and by others.

Complex networks such as the World Wide Web, the web of human sexual contacts, or criminal networks often do not have an engineered architecture but instead are self-organized by the actions of a large number of individuals. From these local interactions nontrivial global phenomena can emerge as small-world properties or scale-free degree distributions. A simple model for the evolution of acquaintance networks highlights the essential dynamical ingredients necessary to obtain such complex network structures. The model generates highly clustered networks with small average path lengths and scale-free as well as exponential degree distributions. It compares well with experimental data of social networks, as for example, coauthorship networks in high energy physics. © 2003 Wiley Periodicals, Inc. Key Words: complex networks; social systems; scaling laws In many kinds of complex systems, large and stable network structures occur. Specific examples include networks of interacting proteins or genes, ecological graphs, communication networks, and social networks [1–4]. For most of them, neither random networks nor regular lattices provide an adequate framework to model the observed topological

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The study of social networks has gained new importance with the recent rise of large online communities. Most current approaches focus on deterministic (descriptive) models and are usually restricted to a preset number of people. Moreover, the dynamic aspect is often treated as an addendum to the static model. Taking inspiration from reallife friendship formation patterns, we propose a new generative model of evolving social networks that allows for birth and death of social links and addition of new people. Each person has a distribution over social interaction spheres, which we term ”contexts. ” We study the robustness of our model by examining statistical properties of simulated networks relative to well known properties of real social networks. We discuss the shortcomings of this model and problems that arise during learning. Several extensions are proposed. 1.

Abstract—In many social networks, the connections between actors are formed because they participate in the same event, such as a set of scholars coauthoring a paper and a person making phone calls or having teleconferences with his friends. Therefore, we propose an event-driven framework for creating network growth models. We also notice that in evolving networks, both the behavior of the whole network and the behavior of nodes evolve over time. For example, we observe in collaborative networks that the growth rates of the communities and the average number of coauthors in papers change as the network sizes increase over time, and researchers ’ interactions with local groups and remote groups also evolve over time with their experience (degree). These observations motivate us to propose a behavior evolution-aware event-driven locality and attachedness based model to capture the growth dynamics in social networks. Based on some informative metrics of network structure and properties, such as degree distribution, degree-dependent clustering coefficients, and degreedependent average degree of neighbors, the experiments suggest that our model can better characterize the growing process and simulate important network structures observed in real networks than other non-event driven and non-behavior aware models. I.

To better represent human interactions in social networks, the authors take a network-oriented simulation approach to analyze the evolution of acquaintance networks based on local interaction rules. Our approach takes into consideration shared friendships, resources, remembering, meetings by chance, and arriving and leaving. Our three main findings are: (a) the topological features of acquaintance networks are affected by initial average values for parameters (i.e., resources, remembering, and number of friendships), but not by their statistical distributions; (b) resources, remembering, and initial friendships positively influence increases in average numbers of friends and decreases in degrees of clustering and separation; and (c) widely used fieldwork sampling methods do not capture the actual node degree distributions of social networks. In addition to confirming the successful use of a network-oriented simulation approach to social network research, the findings indicate a strong need for an approach that stresses interactive rules and “what-if ” type simulation experiments.