Generalized blockmodeling of valued networks

The paper presents several approaches to generalized blockmodeling of valued networks, where values of the ties are assumed to be measured on at least interval scale. The first approach is a straightforward generalization of the generalized blockmodeling of binary networks [Doreian, P., Batagelj, V., Ferligoj, A., 2005. Generalized Blockmodeling. Cambridge University Press, New York.] to valued blockmodeling. The second approach is homogeneity blockmodeling. The basic idea of homogeneity blockmodeling is that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values. New ideal blocks appropriate for blockmodeling of valued networks are presented together with definitions of their block inconsistencies.     

Direct blockmodeling of valued and binary networks: a dichotomization-free approach

A long-standing open problem with direct blockmodeling is that it is explicitly intended for binary, not valued, networks. The underlying dilemma is how empirical valued blocks can be compared with ideal binary blocks, an intrinsic problem in the direct approach where partitions are solely determined through such comparisons. Addressing this dilemma, valued networks have either been dichotomized into binary versions, or novel types of ideal valued blocks have been introduced. Both these workarounds are problematic in terms of interpretability, unwanted data reduction, and the often arbitrary setting of model parameters.This paper proposes a direct blockmodeling approach that effectively bypasses the dilemma with blockmodeling of valued networks. By introducing an adaptive weighted correlation-based criteria function, the proposed approach is directly applicable to both binary and valued networks, without any form of dichotomization or transformation of the valued (or binary) data at any point in the analysis, while still using the conventional set of ideal binary blocks from structural, regular and generalized blockmodeling.The proposed approach seemingly solves two other open problems with direct blockmodeling. First, its standardized goodness-of-fit measure allows for direct comparisons across solutions, within and between networks of different sizes, value types, and notions of equivalence. Secondly, through an inherent bias of point-biserial correlations, the approach puts a premium on solutions that are closer to the mid-point density of blockmodels. This, it is argued, translates into solutions that are more intuitive and easier to interpret.The approach is demonstrated by structural, regular and generalized blockmodeling applications of six classical binary and valued networks. Finding feasible and intuitive optimal solutions in both the binary and valued examples, the approach is proposed not only as a practical, dichotomization-free heuristic for blockmodeling of valued networks but also, through its additional benefits, as an alternative to the conventional direct approach to blockmodeling.     

A deviational approach to blockmodeling of valued networks

This article proposes a novel approach to blockmodeling of valued (one-mode) networks where the identification of (binary) block patterns in the valued relations differ from existing approaches. Rather than looking at the absolute values of relations, or examining valued ties on a per-actor basis (cf. Nordlund, 2007), the approach identifies prominent (binary) ties on the basis of deviations from expected values. By comparing the distribution of each actor's valued relations to its alters with the macro-level distributions of total in- and outdegrees, prominent (1) and non-prominent (0) ties are determined both on a per-actor-to-actor and a per-actor-from-actor basis. This allows for a direct interpretation of the underlying functional anatomy of a non-dichotomized valued network using the standard set of ideal blocks as found in generalized blockmodeling of binary networks.In addition to its applicability for direct blockmodeling, the article also suggests a novel indirect measure of deviational structural equivalence on the basis of such deviations from expected values.Exemplified with the note-sharing data in Žiberna (2007a), citations among social work journals (Baker, 1992), and total commodity trade among EU/EFTA countries as of 2010, both the direct and indirect approach produce results that are more sensitive to variations at the dyadic level than existing approaches. This is particularly evident in the case of the EU/EFTA trade network, where the indirect approach yields partitions and blockmodels in support of theories of regional trade, despite the significantly skewed valued degree distribution of the dataset.     

Money as a Tool for Negotiating Separateness and Connectedness in the Therapeutic Relationship

It is nothing new to suggest that money has meaning. Whether or not one accepts Freud's (1908)linkage of money and feces, within our culture money is frequently seen as a direct pathway to feelings of power, agency, self-directedness, and personal satisfaction. Trachtman (1999) states, Money, psychologically speaking, is our projection onto coins, bills, bank accounts, and other financial instruments of our beliefs, hopes, and fears about how those things will affect who we are, what will happen to us, and how we will be treated by others or by ourselves...(Trachtman, 1999, p. 283). Yet this material is often unavailable for therapeutic exploration or understanding until it explodes into the therapy, often in unmanageable and countertherapeutic ways. This article will look at some of the ways in which money can be utilized to negotiate the ever-changing tensions between self and other, object and subject, intrapyschic and interpersonal, connection and separation that appear in every relationship. In particular, it will explore some ways that money issues within the therapeutic relationship can be turned into significant tools for understanding and working with anxieties about connection and separateness, both within and outside the therapeutic dyad.     

Efficiency and stability in a model of wireless communication networks

We introduce a model of (wireless communication) networks: a group of agents want to communicate with each other; an agent has his own position, chooses his costly communication range, and benefits from direct and indirect communications with other agents; any two agents can directly communicate if each agent is located within another agent’s communication range; they can indirectly communicate if each agent is connected to another agent through a sequence of direct communications. Although efficiency and stability are not compatible in a general context, we identify interesting subclasses of problems where an efficient and stable network exists: the uniform interval model, the uniform circle model, and the communication favorable domain. We also investigate the consequence of allowing agents to relocate their positions. For certain networks, relocation-proofness is equivalent to stability.     

A Nash bargaining model for simple exchange networks

Starting from exogenously given negotiation networks, sociological exchange theories explain bilateral divisions of fixed surpluses (e.g., cake, dollar) as consequences of the partners’ structural embeddedness. In accordance with the available experimental evidence, we focus on simple exchange networks and present a formal model for predicting profit splits from such structures. In contrast to other approaches, we combine the generalized Nash bargaining solution from game theory with the assumption that both relational features and network positions affect exchange outcomes. The resulting point predictions for profit splits correspond closely with experimental results obtained by Cook et al. [Cook, K.S., Emerson, R.M., Gillmore, M.R., Yamagishi, T., 1983. The distribution of power in exchange networks: theory and experimental results. American Journal of Sociology 89, 275–305], Lovaglia et al. [Lovaglia, M.J., Skvoretz, J., Willer, D., Markovsky, B., 1995. Negotiated exchanges in social networks. Social Forces 74, 123–155], Markovsky et al. [Markovsky, B., Willer, D., Patton, T., 1988. Power relations in exchange networks. American Sociological Review 53, 220–236], Simpson and Willer [Simpson, B., Willer, D., 1999. A new method for finding power structures. In: Willer, D. (Ed.), Network Exchange Theory. Praeger, Westport, CT, pp. 270–284], Skvoretz and Fararo [Skvoretz, J., Fararo, T.J., 1992. Power and network exchange: an essay toward theoretical unification. Social Networks 14, 325–344], Skvoretz and Willer [Skvoretz, J., Willer, D., 1993. Exclusion and power: a test of four theories of power in exchange networks. American Sociological Review 58, 801–818] as well as Yamagishi et al. [Yamagishi, T., Gillmore, M.R., Cook, K.S., 1988. Network connections and the distribution of power in exchange networks. American Journal of Sociology 93, 833–851].     

Actor non-response in valued social networks: The impact of different non-response treatments on the stability of blockmodels

Social network data usually contain different types of errors. One of them is missing data due to actor non-response. This can seriously jeopardize the results of analyses if not appropriately treated. The impact of missing data may be more severe in valued networks where not only the presence of a tie is recorded, but also its magnitude or strength. Blockmodeling is a technique for delineating network structure. We focus on an indirect approach suitable for valued networks. Little is known about the sensitivity of valued networks to different types of measurement errors. As it is reasonable to expect that blockmodeling, with its positional outcomes, could be vulnerable to the presence of non-respondents, such errors require treatment. We examine the impacts of seven actor non-response treatments on the positions obtained when indirect blockmodeling is used. The start point for our simulation are networks whose structure is known. Three structures were considered: cohesive subgroups, core-periphery, and hierarchy. The results show that the number of non-respondents, the type of underlying blockmodel structure, and the employed treatment all have an impact on the determined partitions of actors in complex ways. Recommendations for best practices are provided.     

Functional specificity in discussion networks: The influence of general and problem-specific networks on health outcomes

Though commonly used in social science research to measure the influence of social networks, the link between discussing “important matters” within networks and the achievement of instrumental ends is frequently unspecified or untested. To address this gap, we explore the consequences of using the general “important matters” approach versus one in which the substance of discussions is directly linked to the outcomes of interest. The egocentric social networks of people experiencing an acute health crisis are examined. We identify the characteristics of and the degree of membership overlap between “important matters” and “health matters” discussants, and explore their relative power in explaining a wide range of health and health services-related outcomes. We find no evidence for the influence of “important matters” networks, while characteristics of “health matters” networks demonstrate a significant effect across all models.     

Examining School Connectedness as a Mediator of School Climate Effects

Researchers have suggested that good‐quality school climates foster a sense of connection to the school and in this way contribute to fewer emotional and behavioral problems. However, few studies have directly assessed the role of school connectedness as a mediator of school climate effects. Using path analysis, this brief report examined whether four aspects of student perceived school climate (cohesion, friction, competition among students, and overall satisfaction with classes) were indirectly associated with subsequent early adolescent conduct problems and depressive symptoms through school connectedness. Participants were four hundred and eighty‐nine 10‐ to 14‐year old middle school students involved in two waves of a study. The results showed that school connectedness mediated the relations between perceived cohesion, perceived friction, and overall satisfaction with classes and subsequent student conduct problems 1 year later. School connectedness was not, however, predictive of subsequent depressive symptoms and thus did not mediate the school climate effects on early adolescent emotional problems.     

A model for collaboration networks giving rise to a power-law distribution with an exponential cutoff

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the “rich get richer” phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein, e-mail, actor and collaboration networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will become inactive. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model empirically by analysing the Mathematical Research collaboration network, the distribution of which has been shown to be compatible with a power law with an exponential cutoff.     

Fuzzy duocentric community detection model in social networks

The main goal of this paper is to present a clustering model to identify duocentric communities in the complex networks. A duocentric community is built around two central nodes which are as close as possible to other nodes, while the central nodes are connected enough to each other to shape the center of the community. To detect such communities, we develop a new objective function based clustering model. The network's nodes are assigned to the duocentric communities by the type-2 fuzzy numbers which indicate the degrees of belonging to the communities by upper and lower membership values. Generated interval type-2 fuzzy membership values by our proposed model are able to determine how much each node belongs to the both central nodes and how it is shared among communities. Also, the compatible verification index with the proposed model is introduced to evaluate and compare the results of the proposed model with the existing approach in the literature. Finally, the performance of the proposed algorithm is validated by detecting duocentric communities in three artificial networks and two real social networks.     

Identifying regular blocks in valued networks: A heuristic applied to the St. Marks carbon flow data,and international trade in cereal products

While the concept of regular equivalence is equally applicable to dichotomous as well as valued networks, the identification of regular blocks in regular blockmodels is somewhat problematic when dealing with valued networks. Applying the standard procedure for identifying ties in such blockmodels, a procedure perhaps most suited for dichotomous networks, does tend to generate block images and reduced graphs that differ from intuitive notions of such structures.     

Optimal connections: strength and distance in valued graphs

We identify some issues in measuring the strongest path connecting pairs of actors that arise in attempts to generalize binary graph concepts to valued graphs. Neither Peay’s path value nor Flament’s path length indicators take into account the costs of interacting via long chains of intermediaries. We proposed two alternative measures of optimal connections between dyads, respectively, dividing each measure by the distance between a pair (number of lines in a path). We illustrate these average path value (APV) and average path length (APL) measures with a hypothetical five-actor valued graph, observing instances where an indirect path may yield a stronger connection than a direct path. Computer programs to calculate these measures out to three steps for small graphs are available on request.     

Whose knowledge is valued: a critical study of knowledge in elementary school textbooks in China

This study critically examines knowledge in elementary school textbooks in China. Language analysis and story‐line analysis are used to examine how the knowledge related to minority groups and how the knowledge related to the Han group are introduced and interpreted. This study finds that the Han knowledge dominates elementary school textbooks in China and that minority knowledge and culture are under‐represented, which demonstrates that the dominant Han group’s knowledge is seen as the ‘truth’ while minority knowledge is seen as backward. Moreover, through the dominant Han group’s selection and construction of school knowledge, the Han group reproduces its ideology and legitimates its hegemonic control over minority groups. Minority knowledge and culture are, therefore, subjugated.     

A comparison of estimators for the network autocorrelation model based on observed social networks

Network autocorrelation models (NAMs) are widely used to study a response variable of interest among subjects embedded within a network. Although the NAM is highly useful for studying such networked observational units, several simulation studies have raised concerns about point estimation. Specifically, these studies have consistently demonstrated a negative bias of maximum likelihood estimators (MLEs) of the network effect parameter. However, in order to gain a practical understanding of point estimation in the NAM, these findings need to be expanded in three important ways. First, these simulation studies are based on relatively simple network generative models rather than observed networks, thereby leaving as an open question how realistic network topologies may affect point estimation in practice. Second, although there has been strong work done in developing two-stage least squares estimators as well as Bayesian estimators, only the MLE has received extensive attention in the literature, thus leaving practitioners in question as to best practices. Third, the performance of these estimators need to be compared using both bias and variance, as well as the coverage rate of each estimator's corresponding confidence or credible interval. In this paper we describe a simulation study which aims to overcome these shortcomings in the following way. We first fit real social networks using the exponential random graph model and used the Bayesian predictive posterior distribution to generate networks with realistic topologies. We then compared the performance of the three different estimators mentioned above.     

Risk management: a general framework for rural development

This paper proposes a new concept of rural development in an uncertain world. The nature of risk and uncertainty is discussed and risk management is defined as a positive model of economic and social behaviour. Some relevant paradigms for rural development are reviewed and evaluated within the general approach of risk management. It is demonstrated that the proposed view of risk management can effectively combine and reconcile different approaches by highlighting their advantages and shortcomings. Departing from a subjective definition of risk management, we progressively include its social dimensions which introduce both complexity and structure into the process of rural development.     

Credulity rather than general trust may increase vulnerability to fraud in older adults: a moderated mediation model

The present study aimed to clarify whether it is credulity or general trust that specifically affects vulnerability to fraud, as well as investigating the mediating role of susceptibility to persuasion and the moderating role of greed in this relationship. 254 Chinese older adults completed measures of credulity, general trust, susceptibility to persuasion, greed, and vulnerability to fraud. The results showed that credulity, but not general trust, was positively correlated with vulnerability to fraud, after controlling for demographic covariates. Susceptibility to persuasion partially mediated the effect of credulity on vulnerability to fraud. In addition, this mediating effect of susceptibility to persuasion was only significant in older adults with higher levels of greed. Our findings suggest that credulity, rather than general trust, is a risk factor in vulnerability to fraud among older adults, and may inform the development of supportive interventions to reduce this population’s risk of falling victim to fraud.     

Trust and partner selection in social networks: An experimentally grounded model

This article investigates the importance of the endogenous selection of partners for trust and cooperation in market exchange situations, where there is information asymmetry between investors and trustees. We created an experimental-data driven agent-based model where the endogenous link between interaction outcome and social structure formation was examined starting from heterogeneous agent behaviour. By testing various social structure configurations, we showed that dynamic networks lead to more cooperation when agents can create more links and reduce exploitation opportunities by free riders. Furthermore, we found that the endogenous network formation was more important for cooperation than the type of network. Our results cast serious doubt about the static view of network structures on cooperation and can provide new insights into market efficiency.