• Social Networks

• rank-based friendship: a connection between two agents, where the probability that person u befriends person v is inversely proportional to the number of people who are closer to u than v is.
• small world experiment: several experiments conducted by Stanley Milgram examining the average path length for social networks of people in the United States. The research was groundbreaking in that it revealed that human society is a small world type network characterized by shorter-than-expected path lengths.
• six degrees of separation: the term coined after the mean distance between two persons in the small world experiment was six.
• 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)

“O trigo está 227% mais caro hoje do que estava há pouco mais de dois anos, em janeiro de 2006; a soja, no período, subiu 132%, e o milho, 157%. O arroz dobrou de preço em três meses. Os dados são assim impressionantes, e a armadilha na qual o mundo entrou é difícil de desarmar: parte do problema é causada pela mudança climática; parte da solução pode aprofundar a mudança climática”.

Miriam Leitão, 17/04/2008.

“As restrições da União Européia são relacionadas à rastreabilidade, ou seja, o monitoramento do trânsito dos bois, do nascimento ao abate. Em novembro do ano passado, algumas fazendas e frigoríficos apresentaram inconformidades que foram relatadas por veterinários da União Européia, em missão oficial”

Agência Brasil, 15 de Fevereiro de 2008.

The evolution of social networks can sometimes be modeled by the use of agent based models, providing insight into the interplay between communication rules, rumor spreading and social structure. Here is an interactive model of rumour spreading, based on rumour spreading from model on Cmol.

Diffusion of innovations theory explores social networks and their role in influencing the spread of new ideas and practices. Change agents and opinion leaders often play major roles in spurring the adoption of innovations, although factors inherent to the innovations also play a role.

Nevertheless, even as an average person may only be able to establish a few strong ties due to possible constraints of human communication channels, Mark Granovetter found in one study that more numerous weak ties can be important in seeking information and innovation. Cliques have a tendency to more homogeneous opinions as well as sharing many common traits. This homophillic tendency was the reason for the members of the cliques to be attracted together in the first place. However, being similar, each member of the clique would also know more or less what the other members knew. To find new information or insights, members of the clique will have to look beyond the clique to its other friends and acquaintances. This is what Granovetter called the “the strength of weak ties”.

Guanxi is a central concept in Chinese society (and other East Asian cultures) that can be summarized as the use of personal influence. Guanxi can be studied from a social network approach.[6]

The small world phenomenon is the hypothesis that the chain of social acquaintances required to connect one arbitrary person to another arbitrary person anywhere in the world is generally short. The concept gave rise to the famous phrase six degrees of separation after a 1967 small world experiment by psychologist Stanley Milgram. In Milgram's experiment, a sample of US individuals were asked to reach a particular target person by passing a message along a chain of acquaintances. The average length of successful chains turned out to be about five intermediaries or six separation steps (the majority of chains in that study actually failed to complete). The methods (and ethics as well) of Milgram's experiment was later questioned by an American scholar, and some further research to replicate Milgram's findings had found that the degrees of connection needed could be higher.[7] Academic researchers continue to explore this phenomenon as Internet-based communication technology has supplemented the phone and postal systems available during the times of Milgram. A recent electronic small world experiment at Columbia University found that about five to seven degrees of separation are sufficient for connecting any two people through e-mail.[8]

The study of socio-technical systems is loosely linked to social network analysis, and looks at relations among individuals, institutions, objects and technologies.

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.

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.

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.

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.

Abstract: The aim of this paper is to investigate the effect of technological opportunities and knowledge tacitness on inter-firm network formation, under two different industry regimes. In the first regime environment is stable and the aim of firms is to exploit knowledge. In this case, they attribute more value to repeated interactions with geographically close firms. In the second regime, there is environmental turbulence, which increases the value of access to novelties from distant partners for the purpose of exploration. The question addressed is, under these regimes how do technological opportunities and knowledge tacitness influence structure of networks? A simulation model is carried out where firms select partners and learn from them, which further shapes their selection process. How the macro structure of the network is shaped from the individual partner selection decisions of firms is analysed. The results reveal that in both regimes richer technological opportunities and higher tacitness generates local and global star firms depending on the parameter range.

Abstract:We live in a ‘‘small world,’’ where two arbitrary people are likely connected by a short chain of intermediate friends. With scant information about a target individual, people can successively forward a message along such a chain. Experimental studies have verified this property in real social networks, and theoretical models have been advanced to explain it. However, existing theoretical models have not been shown to capture behavior in real-world social networks. Here, we introduce a richer model relating geography and social-network friendship, in which the probability of befriending a particular person is inversely proportional to the number of closer people. In a large social network, we show that one-third of the friendships are independent of geography 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.

Objective: The objective of this study was to examine the relationship between social distance (measured as the geodesic, or shortest distance, between 2 people in a connected network) and geographic distance (measured as the actual distance between them in kilometers [km]).

Study: We used data from a study of 595 persons at risk for HIV and their sexual and drug-using partners (total N = 8920 unique individuals) conducted in Colorado Springs, Colorado, from 1988 to 1992—a longitudinal cohort study that ascertained sociodemographic, clinical, behavioral, and network information about participants. We used place of residence as the geographic marker and calculated distance between people grouped by various characteristics of interest.

Results: Fifty-two percent of all dyads were separated by a distance of 4 km or less. The closest pairs were persons who both shared needles and had sexual contact (mean ~ 3.2 km), and HIV-positive persons and their contacts (mean ~ 2.9). The most distant pairs were prostitutes and their paying partners (mean ~ 6.1 km). In a connected subset of 348 respondents, almost half the persons were between 3 and 6 steps from each other in the social network and were separated by a distance of 2 to 8 km. Using block group centroids, the mean distance between all persons in Colorado Springs was 12.4 km compared with a mean distance of 5.4 km between all dyads in this study (P <0.0001). The subgroup of HIV-positive people and their contacts was drawn in real space on a map of Colorado Springs and revealed tight clustering of this group in the downtown area.

Conclusion: The association of social and geographic distance in an urban group of people at risk for HIV provides demonstration of the importance of geographic clustering in the potential transmission of HIV. The proximity of persons connected within a network, but not necessarily known to each other, suggests that a high probability of partner selection from within the group may be an important factor in maintenance of HIV endemicity.

Abstract: In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000–2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005.

Abstract: Nearly all industries exhibit geographic concentration. Most theories of the location of industry explain the persistence of these production centers as the result of economic efficiency. This article argues instead that heterogeneity in entrepreneurial opportunities, rather than differential performance, maintains geographic concentration. Entrepreneurs need exposure to existing organizations in the industry to acquire tacit knowledge, obtain important social ties, and build self-confidence. Thus, the current geographic distribution of production places important constraints on entrepreneurial activity. Due to these constraints, new foundings tend to reify the existing geographic distribution of production. Empirical evidence from the shoe industry supports this thesis.

Abstract: This paper examines the innovative ability of small firms in the semiconductor industry regarding their exploration of technological diversity and their integration within local knowledge networks. Through the analysis of patent data, we compare the innovative activity of start-up firms and larger firms. We find that small firms explore new technological areas by innovating in less lsquocrowdedrsquo areas. The analysis of patent citation data reveals that small firms are tied into regional knowledge networks to a greater extent than large firms. These findings point to the role of entrepreneurial firms in the exploration of new technological spaces and in the diffusion of their accumulated knowledge through local small firm networks.

Abstract: When a pair of individuals is central to a research problem (e.g., husband and wife, PhD student and supervisor) the concept of “duocentered” networks can be defined as a useful extension of egocentered networks. This new structure consists of a pair of central egos and their direct links with alters, instead of just one central ego as in the egocentered networks or multiple egos as in complete networks. The key point in this kind of network is that ties exist between the central pair of egos and between them and all alters, but the ties among alters are not considered. Duocentered networks can also be considered as a compromise between egocentered and complete networks. Complete network measurements are often costly to obtain and tend to contain a large proportion of missing data (especially for peripheral actors). Egocentered network data are less costly but a lot of information is lost with their use when a pair of individuals is the relevant unit of analysis. From the definition of duocentered networks, we develop new social network measures, some of which based on the measures for complete networks such as degree, closeness centrality or density, both absolute and relative, while others are tailored to dealing with specific characteristics of the duocentered network structures. The proposed measures are used in the analysis of the networks of Slovenian PhD students and their supervisors. We specify three regression models to predict PhD student’s academic performance on the basis of these duocentered network measures for different relations such as advice, collaboration, emotional support, and trust. The results show that absolute duocentered measures predict performance best. When compared with egocentered network measures a higher predictive power of duocentered networks is revealed.

Rising international cooperation, vertical disintegration, along with a focus on core activities have led to the notion that firms are links in a networked supply chain. This novel perspective has created the challenge of designing and managing a network of interdependent relationships developed and fostered through strategic collaboration. Although research interests in supply chain management (SCM) are growing, no research has been directed towards a systematic development of SCM instruments.

This study identifies and consolidates various supply chain initiatives and factors to develop key SCM constructs conducive to advancing the field. To this end, we analyzed over 400 articles and synthesized the large, fragmented body of work dispersed across many disciplines. The result of this study, through successive stages of measurement analysis and refinement, is a set of reliable, valid, and unidimensional measurements that can be subsequently used in different contexts to refine or extend conceptualization and measurements or to test various theoretical models, paving the way for theory building in SCM.

Abstract: We study a supply chain economy (SCE) that comprises heterogeneous SC involving multiple products and competing for multiple markets. The proposed network model is built upon operation links and interface links, representing, respectively, substantial SC operations and coordination functions between the operations. The paper presents a variational inequality formulation of the problem, the solution of which determines the winning SC and their market shares in the equilibrium of SCE. We furnish qualitative properties such as existence and uniqueness of the equilibrium. Numerical examples are presented for illustrative purpose.

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.

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.