Hawoong Jeong

The large-scale organization of metabolic networks.

In a cell or microorganism, the processes that generate mass, energy, information transfer and cell-fate specification are seamlessly integrated through a complex network of cellular constituents and reactions. However, despite the key role of these networks in sustaining cellular functions, their large-scale structure is essentially unknown. Here we present a systematic comparative mathematical analysis of the metabolic networks of 43 organisms representing all three domains of life. We show that, despite significant variation in their individual constituents and pathways, these metabolic networks have the same topological scaling properties and show striking similarities to the inherent organization of complex non-biological systems. This may indicate that metabolic organization is not only identical for all living organisms, but also complies with the design principles of robust and error-tolerant scale-free networks, and may represent a common blueprint for the large-scale organization of interactions among all cellular constituents.

Lethality and centrality in protein networks.

Proteins are traditionally identified on the basis of their individual actions as catalysts, signalling molecules, or building blocks in cells and microorganisms. But our post-genomic view is expanding the proteins role into an element in a network of protein–protein interactions as well, in which it has a contextual or cellular function within functional modules. Here we provide quantitative support for this idea by demonstrating that the phenotypic consequence of a single gene deletion in the yeast Saccharomyces cerevisiae is affected to a large extent by the topological position of its protein product in the complex hierarchical web of molecular interactions.

Evolution of the social network of scientific collaborations

The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it offers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the networks time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks.

Internet: Diameter of the World-Wide Web

Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the webs connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.

Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.

Scale-free characteristics of random networks: the topology of the world-wide web

The world-wide web forms a large directed graph, whose vertices are documents and edges are links pointing from one document to another. Here we demonstrate that despite its apparent random character, the topology of this graph has a number of universal scale-free characteristics. We introduce a model that leads to a scale-free network, capturing in a minimal fashion the self-organization processes governing the world-wide web.

Analysis of topological characteristics of huge online social networking services

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 Cyworlds 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 datas 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 e ponents corresponds to the different segments in Cyworlds 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.

Modeling the Internet's large-scale topology

Network generators that capture the Internets large-scale topology are crucial for the development of efficient routing protocols and modeling Internet traffic. Our ability to design realistic generators is limited by the incomplete understanding of the fundamental driving forces that affect the Internets evolution. By combining several independent databases capturing the time evolution, topology, and physical layout of the Internet, we identify the universal mechanisms that shape the Internets router and autonomous system level topology. We find that the physical layout of nodes form a fractal set, determined by population density patterns around the globe. The placement of links is driven by competition between preferential attachment and linear distance dependence, a marked departure from the currently used exponential laws. The universal parameters that we extract significantly restrict the class of potentially correct Internet models and indicate that the networks created by all available topology generators are fundamentally different from the current Internet.

The diameter of the world wide web

Despite its increasing role in communication, the World-Wide Web remains uncontrolled: any individual or institution can create a website with any number of documents and links. This unregulated growth leads to a huge and complex web, which becomes a large directed graph whose vertices are documents and whose edges are links (URLs) that point from one document to another. The topology of this graph determines the webs connectivity and consequently how effectively we can locate information on it. But its enormous size (estimated to be at least 8×108 documents) and the continual changing of documents and links make it impossible to catalogue all the vertices and edges.

Measuring preferential attachment in evolving networks

A key ingredient of many current models proposed to capture the topological evolution of complex networks is the hypothesis that highly connected nodes increase their connectivity faster than their less connected peers, a phenomenon called preferential attachment. Measurements on four networks, namely the science citation network, Internet, actor collaboration and science coauthorship network indicate that the rate at which nodes acquire links depends on the nodes degree, offering direct quantitative support for the presence of preferential attachment. We find that for the first two systems the attachment rate depends linearly on the node degree, while for the last two the dependence follows a sublinear power law.