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Topic: Scale-free network

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Search Encyclopedia.com Beaufort scale Beaufort scale, a scale of wind velocity devised (c.1805) by Admiral Sir Francis Beaufort of the British navy. free energy free energy or Gibbs free energy, quantity derived from the relationships between heat and work studied in thermodynamics and used as a measure of the relative stability of a physical or chemical system, i.e., the tendency of the system to react or change. scale scale, in zoology, an outgrowth, either bony or horny, of the skin of an animal. www.encyclopedia.com /searchpool.asp?target=scale+free+network

Scale-free network - Wikipedia, the free encyclopedia In scale-free networks, some nodes act as "highly connected hubs" (high degree), although most nodes are of low degree. A scale-free network is a specific kind of complex network that has attracted attention since many real-world networks fall into this category. These networks also exhibit the Small world phenomenon, in which two average nodes are separated by a very small number of connections. en.wikipedia.org /wiki/Scale-free_network

Asynchronous discussion groups as Small World and Scale Free Networks On Scale Free networks, the distribution of density or congestion is constant and is not dependent on the exponential coefficient of the distribution of the number of connections (Jeong, 2003). The exponents displayed in Table 2 and in Figures 1–3 indicate that indeed the network is a Scale Free network, because its degree is exponentially distributed. Scale Free nets are characterized by the fact that most people have few contacts and a small part of the people have extremely many contacts. www.firstmonday.org /issues/issue9_9/ravid/index.html

The Ultimate Complex network - American History Information Guide and Reference A network with a single scale is similar to grid: every node has the same degree or the same number of links/edges. A network is called small-world network by analogy with the small-world phenomenon, (popularly known as six degrees of separation). They are special networks at the edge of chaos where the degree of connectivity is neither regular nor random. www.historymania.com /american_history/Complex_network

Clearing up the market cycle... best Scale-Free Network A scale-free network is a specific kind of network in which the distribution of connectivity is extremely uneven. Extremum statistics in scale-free network models Extremum statistics in scale-free network models We investigate the statistics of the most connected nodes in scale-free networks. Scale Free Network what we do...why we exist....how we work.. ascot.pl /th/Fourier5/Scale-Free-Network.htm

The KAIST Herald However, the study of networks in association with the real-world networks such as information systems, economic systems, and biological systems are quite recent trends. Modeling random networks has a long history, and has been particularly active as a branch of combinatorial graph theory. He studies complex systems and statistical physics, and recently he mainly researches about modeling networks. herald.kaist.ac.kr /science/0312s1.html

Cafe Kaboom In a scale free network, the behavior of all the nodes should be study as unison, since the links among nodes are governed by power law; most of the nodes have few links and they are held together by a large hub. While scale-free network explains how there are rules behind complexity, power law is the center guide of the functionality of a scale-free network. Scale-free network has a unique nature, earlier a node appears in the network, more likely it can obtain more links. kabunmon.blogspot.com /2002_10_20_kabunmon_archive.html

Box 2 The community of the self : Nature Distances between nodes are, on average, smaller in scale-free (SF) networks than in exponential (E) networks that connect equal numbers of nodes (see distance at zero failure). In the scale-free network, most nodes have only a few links, but a few nodes, called hubs (dark blue), have a very large number of links. Once the network has failed, restoration of function to key affected nodes is necessary, but the appropriate connections must be restored to ensure resurrection of function. www.nature.com /nature/journal/v420/n6912/box/nature01260_bx2.html

Citebase - Geography in a Scale-Free Network Model @article{warren-2002-66, author = {C P Warren and L M Sander and I M Sokolov}, title = {Geography in a Scale-Free Network Model}, journal = {Physical Review E}, volume = {66}, pages = {056105}, url = {http://arxiv.org/abs/cond-mat/0207324}, year = {2002} } We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We study spatial networks constructed by randomly placing nodes on a manifold and joining two nodes with an edge whenever their distance is less than a certain cutoff. citebase.eprints.org /cgi-bin/citations?id=oai%3AarXiv%2Eorg%3Acond%2Dmat%2F0207324

The stomatal scale This means that unlike, a random network in which each component (or node) is connected to each other by roughly the same number of connections, the scale-free network possesses a very small number of highly connected nodes or hubs. When we advanced the hypothesis that stomatal signalling exhibited properties reminiscent of scale-free networks our evidence was based on the known emergent properties of the system and a limited amount of information about the individual components present in the system (Hetherington and Woodward 2003). A scale-free network is defined by its degree of connectivity. bssv01.lancs.ac.uk /bs/pgadmit/PgProjects/amh1.htm

Howardisms: Ranking People in a Scale-Free Network Far from being just a geeky concept, scale-free networks are patterns that have deep importance for everyone … Allow me to demonstrate. Just read this article in Scientific American about the qualities of a network of relationships … don't worry, I won't loose you, gentle reader, in a fury of mathematical jargon … in fact, even the original article wasn't too deep. I think a lot of us used to think that social relationships were kind of like a "highway system" for whether you were a huge city or a small one, you didn't necessarily have more highways just because of your size. www.howardism.org /thoughts/000529.html

Citebase - Random model for RNA interference yields scale free network The model spontaneously yields a scale free network with power law scaling with $ \gamma=-1$ and also exhibits log-periodic behaviour. Random model for RNA interference yields scale free network The network is of the smallest world type, with the average minimum path length independent of the size of the network, as long as the network consists of one giant cluster. citebase.eprints.org /cgi-bin/citations?id=oai%3AarXiv%2Eorg%3Aq%2Dbio%2F0310027

PRL02B In contrast to other scale-free networks, where the topology results from the dynamics of the network growth, the potential energy landscape is a static entity. We find that this network has both a small-world and scale-free character. Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. www-doye.ch.cam.ac.uk /abstracts/prl02b.html

CiteULike: Two complementary representations of a scale-free network Several studies on real complex networks from different fields as biology, economy, or sociology have shown that the degree of nodes (number of edges connected to each node) follows a scale-free power-law distribution like $P(k)≈ k^-γ$, where $P(k)$ denotes the frequency of the nodes that are connected to $k$ other nodes. Here we have carried out a study on scale-free networks, where a line graph transformation (i.e., edges in an initial network are transformed into nodes) is applied on a power-law distribution. Our results indicate that a power-law distribution as $P(k)≈ k^-γ +1$ is found for the transformed network together with a peak for low-degree nodes. www.citeulike.org /user/nettraq/article/596

IngentaConnect Scale-free network on Euclidean space optimized by rewiring of li... A Barabási-Albert scale-free network is constructed whose nodes are the Poisson distributed random points within a unit square and links are the straight line connections among the nodes. The resulting optimized network has a small diameter as well as high clustering and the link-length distribution has a stretched exponential tail. The cost function, which is the total wiring length associated with such a network defined on a two-dimensional plane, is optimized. api.ingentaconnect.com /content/iop/jphysa/2003/00000036/00000019/art00101

scalefree: What is a scale free network ? In a nutshell, a scale-free network is a network where links between nodes aren't added or distributed randomly. This article - Scale Free Networks offers up a good explanation. Applied to the internet, you see this in super-connected sites such as Yahoo, Google, etc. In a social networking model, these hubs are generally known as "connectors", and are normally responsible for bringing together disparate groups. www.scalefree.info /2003/12/what_is_a_scale.html

ScaleFree.Net: First Monday: YASFN (Yet Another Scale Free Network) article This month's lead article is titled Asynchronous Discussion Groups as Small World and Scale Free Networks. The authors took a set of online discussion groups at a university, combined them into a single dataset & did an analysis of who replied to whom; the result proved to be a network that was both scale-free & small world. In a self organized network, centrality is determined by fitness, not seniority. scalefree.net /archives/000166.html

Smart Mobs: Scale-free network searching Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. www.smartmobs.com /archive/2003/05/23/scalefree_netw.html

Figure 1 Although in the exponential network only 27% of the nodes are reached by the five most connected nodes, in the scale-free network more than 60% are reached, demonstrating the importance of the connected nodes in the scale-free network Both networks contain 130 nodes and 215 links ( b, The scale-free network is inhomogeneous: the majority of the nodes have one or two links but a few nodes have a large number of links, guaranteeing that the system is fully connected. The network visualization was done using the Pajek program for large network analysis: www.nature.com /nature/journal/v406/n6794/fig_tab/406378a0_F1.html

Boolean Dynamics This is a project investigating the behavior of a Boolean network with a scale-free architecture. Looking at several behaviors of networks as a function of degree exponent (behavior of individual nodes, number of change events) Current work on finding analytical justification for number of changes distributions in networks (very messy at the moment) (nb) (PDF) www.nd.edu /~astrathm/boolean_dynamics_on_scale_free_network.htm

The Collective Dynamics of Social Systems:Designing Evolutionary Change - Course Topics Several workers have sought to characterize the mechanism responsible for the emergence of scale-free networks, that is, to characterize the dynamics of scale-free network formation. This territory lies between two limiting case topologies, (1) highly connected networked regular lattices, where remote nodes are connected by many short jumps, typical of cellular automata for example, and (2) networks connected at random, in which distant points can sometimes be reached in a single jump, but there may be little connection between neighbors. For a random network P(k) peaks strongly at k = and decays exponentially for large k (that is, P(k)*e-k for k >> and k << ). www.ceu.hu /envsci/corliss/course/05_Nets_Connectivity.html

Scale-free network of earthquakes It is discovered that an evolving random graph associated with earthquakes behaves as a scale-free network of the Barabási-Albert type. The distributions of connectivities in the graphs thus constructed are found to decay as a power law, showing a novel feature of earthquake as a complex critical phenomenon. In this way, the seismic data are mapped to a random graph. www.edpsciences.org /articles/epl/abs/2004/04/epl8017/epl8017.html

hakank.blogg: Scale-Free Network Business Development Strategy They are all networks of nodes that interact with each other and the shape of these networks all have the same scale-free characteristics. Scale-free network has few hubs that connect vast numbers of nodes and a large number of nodes that has very few connections. This paper examines how to apply scale-free network in business development, and use it to grow the business into unbeatable success. www.hakank.org /webblogg/archives/000664.html

Dante's weblog A scale free network is a natural consequence of the ever-expanding nature of real networks. It is interesting that through the talk of networks mathematicians and physicists can be related to them. The theories of Erdos and Renyi are very interesting but they only apply to fixed networks and not ones that grow. www.danchan.com /weblog/Dante/47563

S0217984904007700 The model shows the characteristics of real networks such as small-world property, high degree of clustering, scale-free behavior in degree distribution, and hierarchical topology. We introduce an evolving complex network model, where a new vertex is added and new edges between already existing vertices are added with a control parameter p. In addition, the clustering coefficient is tunable by changing the control parameter p, and the average path length L is proportional to ln(ln N) with nonzero p, where N is the network size. dx.doi.org /10.1142/S0217984904007700

Modelling virus propagation in a scale free network model To write a computer program that generates a network with scale free properties. This project is done as part of the course In765 Knowledge Networks at the University College of Molde. The idea of this project has been rolling around in the back of my head for quite some time but somehow the time to start it and do it has not appeared on its own. home.himolde.no /~molka/in765/Hellesvik-outline.htm

Site Contents at the free Online Encyclopedia. You are here: Online Encyclopedia > Site Map pg 6 > Scale-free network through Scientific misconduc... In a household, clothes hangers are the single one item that you own the most of, yet no one can name even one brand? Enter a phrase or search word in the box below. www.onlineencyclopedia.org /index_286.html

Research at HP Labs : Information Dynamics Lab : Papers : A social network caught in the Web We observed and measured social network phenomena such as the small world effect, clustering, and the strength of weak ties. Using the rich profile data provided by the users we were able to deduce the attributes contributing to the formation of friendships, and to determine how the similarity of users decays as the distance between them in the network increases. In addition, we found correlations between a user's personality and their other attributes, as well as interesting correspondences between how users perceive themselves and how they are perceived by others. www.hpl.hp.com /shl/papers/social/index.html

S012918310400639X In this paper we study the model of opinion dynamics with individuals on nodes of a scale-free network, introducing an opinion evolution mechanism and according to the nodes' degrees defining broad-sense-concept leaders on the network. With computer simulations of opinion dynamics, we found that the more complex is the scale-free network, the easier for leaders to make their opinion accepted by the masses. OPINION EVOLUTION ON A SCALE-FREE NETWORK WITH LEADERS dx.doi.org /10.1142/S012918310400639X

Math Awareness Month April 2004 Poster, Image #10 Scale-free diagram courtesy of Dennis Bray, "Molecular Networks: The Top-Down View," Science, Vol. Mathematics Awareness Month is sponsored each year by the Joint Policy Board for Mathematics to recognize the importance of mathematics through written materials and an accompanying poster that highlight mathematical developments and applications in a particular area. www.mathaware.org /mam/04/10_scale-free_network.html

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