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--- geopro:pedro:networks [2008/05/05 19:20] – pedro
+++ geopro:pedro:networks [2009/03/30 17:10] (atual) – pedro
@@ Linha 13: / Linha 13: @@
   * **Erdős number:** is a way of describing the "collaborative distance", in regard to mathematical papers, between an author and Paul Erdős, one of the most prolific writers of mathematical papers.
   * **Dunbar's number:** the typical size of a social network is constrained to about 150 members due to possible limits in the capacity of the human communication channel.
+  * **social distance:** the shortest number of steps between 2 persons in a network.
+  * **Fruchterman-Reingold algorithm**: Graph Drawing by Force-directed Placement (1991)
+  * **Boolean network:** a set of Boolean variables whose state is determined by other variables in the network. They are a particular case of discrete dynamical networks, where time and states are discrete, i.e. they have a bijection onto an integer series. Boolean and elementary cellular automata are particular cases of Boolean networks.
 =====Motivation=====
@@ Linha 32: / Linha 35: @@
 {{  http://www.leg.ufpr.br/~pedro/figures/network-infoflow.jpg}}
 =====Papers=====
@@ Linha 52: / Linha 56: @@
-====The Spatial Structure of Networks====
-|M. T. Gastner and M. E. J. Newmann, 2006| European Physical Journal B 49, 247-252|
-\\
-**Abstract:** We study **networks that connect points in geographic space**, such as transportation networks and the Internet. We find
-that **there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from
-one another and from non-geographic networks**. We offer an explanation of these differences in terms of the costs and benefits of
-transportation and communication, and give a simple model based on Monte Carlo optimization of these costs and benefits that reproduces
-well the qualitative features of the networks studied.
-Internet and airline networks are not really two-dimensional at all, but the road network is.
-|                         ^  Internet    ^  airlines   ^  highway  |
-^vertices                 |  7049 computers  |  187 airports  |  935 intersections, termination points, and country borders  |
-^edges                    |  13831 links  |  825 scheduled flights  |  1337 highway stretches  |
-^diameter                 |  8  |   3  |  61  |
-^degree of the vertices   |  2138 (30%)  |  141 (76%)  |  4 (0,4%)  |
-^peaks on the distribution  |  two  |  two  |   one  |
-Why do not use cities as vertices of a highway instead of intersections, termination points and country borders?
-Future work: the effects of population distribution on the networks, and vice-versa.
-====Collective dynamics of `small-world' networks====
-|Watts, D J and Strogatz, S H, 1998| Nature  393(6684) 440-442|
-\\
-**Abstract:** Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays,, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks `rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them `small-world' networks, by analogy with the small-world phenomenon, (popularly known as six degrees of separation). The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.
-\\
-====The Strength of Weak Ties====
-|M. S. Granovetter| Americal Journal of Sociology, 1973 78(6) 1360-1380| [[http://www.stanford.edu/dept/soc/people/mgranovetter/documents/granstrengthweakties.pdf|pdf]]|
-{{  http://www.leg.ufpr.br/~pedro/figures/bridges.jpg}}
-\\
-**Abstract:** Analysis of social networks is suggested as a tool for linking micro and macro levels of sociological theory. The procedure is illustrated by elaboration of the macro implications of one aspect of small-scale interaction: **the strength of dyadic ties. It is argued that the degree of overlap of two individuals' friendship networks varies directly with the strength of their tie to one another. The impact of this principle on diffusion of influence and information, mobility opportunity, and community organization is explored.** Stress is laid on the cohesive power of weak ties. Most network models deal, implicitly, with strong ties, thus confining their applicability to small, well-defined groups. Emphasis on weak ties lends itself to discussion of relations //between// groups and to analysis of segments of social structure not easily defined in terms of primary groups.
-\\
-**The strength of a tie is a (probabily linear) combination of the amount of time, the emotional intensity, the intimacy (multual confiding), and the reciprocal services which characterize the tie.** Ties are strong, weak, or absent. The stronger the tie between A and B, the larger the proportion of S to whom they will both be tied. The hypothesis is made plausible also by empirical evidence that the stronger the tie connecting two individuals, the more similar they are, in various ways.
-In the figure, A-B is a local bridge of degree 3 (above), and of degree 13 (below). As higher is the degree, stronger is the bridge. By the same logic used above, only weak ties may be local bridges.
-Tells about the problem of a participant observation to get information of a fairy restricted circle, and therefore do not take into account the weak ties.
@@ Linha 112: / Linha 70: @@
 \\
+====Scale-free network of a dengue epidemic====
-====Geographic routing in social networks====
+|E Massad, S Ma, M Chen, C J Struchiner, N Stollenwerk, M Aguiar, 2008| Applied Mathematics and Computation 195:376–381| [[http://www.leg.ufpr.br/~pedro/papers/amc/network-dengue.pdf|pdf]]|
-{{ http://www.leg.ufpr.br/~pedro/figures/distance-and-friendship2.jpg}}
-|D Liben-Nowel, J Novak, R Kumar, P Raghavan, and A Tomkins, 2005| PNAS 102(33)  11623–11628| [[http://www.leg.ufpr.br/~pedro/papers/pnas/geographic-routing-social-networks.pdf|pdf]]|
 \\
-**Abstract:**We live in a ‘‘small world,’’ where two arbitrary people are likely connected by a short chain of intermediate friends. With scant
+**Abstract:** In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of
-information about a target individual, people can successively forward a message along such a chain. Experimental studies have
+transmission as the 2000–2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding
-verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing
+places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization
-theoretical models have not been shown to capture behavior in real-world social networks. Here, we introduce a richer model
+of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our
-relating geography and social-network friendship, in which the probability of befriending a particular person is inversely proportional
+hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which
-to the number of closer people. In a large social network, we show that one-third of the friendships are independent of geography
+evolved towards a power law as the epidemic intensity progressed until 2005.
-and the remainder exhibit the proposed relationship. Further, we prove analytically that short chains can be discovered in
-every network exhibiting the relationship.
 \\
-at first blush, geographic location might have very little to do with the identity of a
-person’s online friends, but Fig. 3A verifies that geography remains crucial in online friendship.
-Although it has been suggested that the impact of distance is marginalized by communications technology
-(26), a large body of research shows that proximity remains a critical factor in effective collaboration and that the negative impacts of
-distance on productivity are only partially mitigated by technology (27). However, for distances larger than 1000 km, the
-curve approximately flattens to a constant probability of friendship between people, regardless of the geographic distance between them.
@@ Linha 189: / Linha 136: @@
 \\
 ====A network economic model for supply chain versus supply chain competition====
@@ Linha 199: / Linha 147: @@
 \\
+====Economic Action and Social Structure: The Problem of Embeddedness====
+|M. Granovetter, 1985| American Journal of Sociology 91:481-510| [[http://www.leg.ufpr.br/~pedro/papers/embeddedness-social-structure-granovetter.pdf|pdf]]|
+\\
+**Abstract:** How behaviour and institutions are affected by social relations is one of the classic
+questions of social theory. This paper concerns the extent to which economic action is embedded in
+structures of social relations, in modern industrial society. Although the usual neoclassical
+accounts provide an "undersocialized" or atomized-actor explanation of such action, reformist
+economics who attempt to bring social structure back in do so in the "oversocialized" way
+criticized by Dennis Wrong. Under- and over socialized accounts are paradoxically similar in their
+neglect of ongoing structures of social relations, and a sophisticated account of economic action
+must consider its embeddedness in such structures. The argument is illustrated by a critic of
+Oliver Willamson's "markets and hierarchies" research program.
+\\
+FIXME Checar a veracidade: the behaviour of individuals cannot be explained except in terms of their
+interaction with other individuals known to them. Individuals being influenced by other individuals
+without slavishly imitating them.
+====Capturing Social Embeddedness: a constructivist approach====
+|B Edmonds, 1999| Adaptive Behaviour 7:323-348| [[http://www.leg.ufpr.br/~pedro/papers/social-embeddedness-constructivist.pdf|pdf]]|
+\\
+**Abstract:** A constructivist approach is applied to characterising social embeddedness. Social embeddedness is
+intended as a strong type of **social situatedness**. It is defined as the extent to which modelling the
+behaviour of an agent requires the inclusion of other agents as individuals rather than as an
+undifferentiated whole. Possible consequences of the presence of social embedding and ways to check
+for it are discussed. A model of co-developing agents is exhibited which demonstrates the possibility of
+social embedding. This is an extension of Brian Arthur’s ‘El Farol Bar’ model, with added learning and
+communication. Some indicators of social embedding are analysed and some possible causes of social
+embedding are discussed. It is suggested that social embeddedness may be an explanation of the causal
+link between the social situatedness of the agent and it employing a constructivist strategy in its
+modelling.
+\\