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21
Problems with fitting to the powerlaw distribution
- Condensed Matter Archive
"... Abstract. This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents ..."
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Abstract. This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new
Human sexual contact network as a bipartite graph. 2002. ArXiV preprint cond-mat/0111323
"... A simple model to encapsulate the essential growth properties of the web of human sexual contacts is presented. In the model only heterosexual connection is considered and represented by a random growing bipartite graph where both male-female contact networks grow simultaneously. The time evolution ..."
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A simple model to encapsulate the essential growth properties of the web of human sexual contacts is presented. In the model only heterosexual connection is considered and represented by a random growing bipartite graph where both male-female contact networks grow simultaneously. The time evolution of the model is analysed by a rate equation approach leading to confirm that the male and the female sexual contact distributions decay as power laws with exponents depending on the influx and the charisma of males and females. PACS numbers: 02.50.cw, 05.40.-a, 89.75Hc. Yet another human interaction network! The web of human sexual contacts is introduced in [1], where the authors make extensive analysis of 1996 Swedish survey of sexual behaviour and show that the cumulative distributions of number of sexual partners for males and females have power law forms with exponents αf ≈ 2.54 for females and αm ≈ 2.31 for
Reciprocity and the Emergence of Power Laws in Social Networks
- International Journal of Modern Physics C
, 2006
"... Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of ..."
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Research in network science has shown that many naturally occurring and technologically constructed networks are scale free, that means a power law degree distribution emerges from a growth model in which each new node attaches to the existing network with a probability proportional to its number of links (=degree). Little is known about whether the same principles of local attachment and global properties apply to societies as well. Empirical evidence from six ethnographic case studies shows that complex social networks have significantly lower scaling exponents γ ∼ 1 than have been assumed in the past. Apparently humans do not only look for the most prominent players to play with. Moreover cooperation in humans is characterized through reciprocity, the tendency to give to those from whom one has received in the past. Both variables – reciprocity and the scaling exponent – are negatively correlated (r = −0.767, sig = 0.075). If we include this effect in simulations of growing networks, degree distributions emerge that are much closer to those empirically observed. While the proportion of nodes with small degrees decreases drastically as we introduce reciprocity, the scaling exponent is more robust and changes only when a relatively large proportion of attachment decisions follow this rule. If social networks are less scale free than previously assumed this has far reaching implications for policy makers, public health programs and marketing alike.
Energy landscapes, scale-free networks and Apollonian packings
- In: Complexity, Metastability and Nonextensivity. 31st Workshop of the International School of Solid State Physics
, 2006
"... We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free character of the inherent structure networks. Namely, that the ener ..."
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We review recent results on the topological properties of two spatial scale-free networks, the inherent structure and Apollonian networks. The similarities between these two types of network suggest an explanation for the scale-free character of the inherent structure networks. Namely, that the energy landscape can be viewed as a fractal packing of basins of attraction. 1.
On reducing terrorism power: a hint from physics
- In Physica A, Volume 323, Elsevier Science B.V. Editors
, 2003
"... The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight agai ..."
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The September 11 attack on the US has revealed an unprecedented terrorism worldwide range of destruction. Recently, it has been related to the percolation of worldwide spread passive supporters. This scheme puts the suppression of the percolation effect as the major strategic issue in the fight against terrorism. Accordingly the world density of passive supporters should be reduced below the percolation threshold. In terms of solid policy, it means to neutralize millions of random passive supporters, which is contrary to ethics and out of any sound practical scheme. Given this impossibility we suggest instead a new strategic scheme to act directly on the value of the terrorism percolation threshold itself without harming the passive supporters. Accordingly we identify the space hosting the percolation phenomenon to be a multi-dimensional virtual social space which extends the ground earth surface to include the various independent terrorist-fighting goals. The associated percolating
Growing Trees in Internet News Groups and Forums
, 2007
"... Abstract. We present an empirical study of the networks created by users within internet news groups and forums and show that they organise themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structur ..."
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Abstract. We present an empirical study of the networks created by users within internet news groups and forums and show that they organise themselves into scale-free trees. The structure of these trees depends on the topic under discussion; specialist topics have trees with a short shallow structure whereas more universal topics are discussed widely and have a deeper tree structure. For news groups we find that the distribution of the time intervals between when a message is posted and when it receives a response exhibits a composite power-law behaviour. From our statistics we can see if the news group or forum is free or is overseen by a moderator. The correlation function of activity, the number of messages posted in a given time, shows long range correlations connected with the users ’ daily routines. The distribution of distances between each message and its root is exponential for most news groups and power-law for the forums. For both formats we find that the relation between the supremacy ( the total number of nodes that are under the node i, including node i) and the degree is linear s(k) ∼ k, in contrast to the analytical relation for Barabási-Albert network. 1
Complex Networks: Statics and Dynamics
, 2000
"... Abstract. We present some of the results obtained during the last 8 years about complex networks. Starting with the collection of data in the form of networks or graphs, we proceed on the characterization at different scales: microscopic, macroscopic, and mesoscopic. We introduce also the basic mode ..."
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Abstract. We present some of the results obtained during the last 8 years about complex networks. Starting with the collection of data in the form of networks or graphs, we proceed on the characterization at different scales: microscopic, macroscopic, and mesoscopic. We introduce also the basic models incorporating complexity in the pattern of connectivities. Finally we review some results on dynamical features on complex networks.
www.elsevier.com/locate/physa Topological properties of integer networks
, 2005
"... Inspired by Pythagoras’s belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fai ..."
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Inspired by Pythagoras’s belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fairly large clustering coefficient C 0:34, which is insensitive to the size of the network. The average distance between two nodes is shown to have an upper bound that is independent of the size of the network, in contrast to the behavior in small-world and ultra-small-world networks. The out-degree distribution is shown to follow a power-law behavior of the form k 2. In addition, these networks possess hierarchical structure as CðkÞ k 1 in accord with the observations of many real-life networks. r 2005 Elsevier B.V. All rights reserved.
unknown title
, 2004
"... Empirical nonextensive laws for the county distribution of total personal income and gross domestic product ..."
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Empirical nonextensive laws for the county distribution of total personal income and gross domestic product
