Network Science — Network Medicine Institute and Alliance

The large-scale organization of metabolic networks

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.

Guest UserOctober 5, 2000Nature

Error and attack tolerance of complex networks

Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneouslywired networks,called scale-free networks, which include theWorld-WideWeb, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates.However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network’s connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.

Guest UserJuly 27, 2000Nature

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.

Guest UserJune 15, 2000Physica

Power-law distribution of the world wide web

Barabasi and Albert propose an improved version of the Erdos-Renyi theory of random networks to account for the scaling properties of a number of systems, including the link structure of the World Wide Web (WWW). The theory they present, however, is inconsistent with empirically observed properties of the Web link structure.

Guest UserJanuary 1, 2000Science

Emergence of scaling in random networks

Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

Guest UserOctober 21, 1999Science

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 web’s connectivity and consequently how effectively we can locate information on it.

Guest UserJanuary 1, 1999Nature