A multiple indicator approach to blockmodeling signed networks

Regardless of whether the focus is on algebraic structures, elaborating role structures or the simple delineation of concrete social structures, generalized blockmodeling faces a pair of vulnerabilities. One is sensitivity to poor quality of the relational data and the other is a risk of over fitting blockmodels to the details of specific networks. Over fitting blockmodels can lead to multiple equally well fitting partitions where choices cannot be made between them on a principled basis. This paper presents a method of tackling these problems by viewing (when possible) observed social relations as multiple indicators of an underlying affect dimension. Quadratic assignment methods using matching coefficients, product moment correlations and Goodman and Kruskal's gamma are used to assess the appropriateness of using the sum of observed relations as input for applying generalized blockmodeling. Data for four groups are used to show the value of this approach within which multiple equally well fitting blockmodels for single relations are replaced by unique (or near-unique) partitions of the summed data. This strategy is located also within a broader problem of blockmodeling three-dimensional networks data and suggestions are made for future work.     

Partitioning large signed two-mode networks: Problems and prospects

While a substantial amount of attention within social network analysis (SNA) has been given to the study of one-mode networks, there is an increasing consideration of two-mode networks. Recent research on signed networks resulted in the relaxed structural balance (RSB) approach and its subsequent extension to signed two-mode networks involving social actors and social objects. We extend this approach to large signed two-mode networks, and address the methodological issues that arise. We develop tools to partition these types of networks and compare them with other approaches using a recently collected dataset of United Nations General Assembly roll call votes. Although our primary purpose is methodological, we take the first step towards bridging Heider's structural balance theory with recent theorizing in international relations on soft balancing of power processes.     

Multiple partitioning of multiplex signed networks: Application to European parliament votes

For more than a decade, graphs have been used to model the voting behavior taking place in parliaments. However, the methods described in the literature suffer from several limitations. The two main ones are that 1) they rely on some temporal integration of the raw data, which causes some information loss; and/or 2) they identify groups of antagonistic voters, but not the context associated with their occurrence. In this article, we propose a novel method taking advantage of multiplex signed graphs to solve both these issues. It consists in first partitioning separately each layer, before grouping these partitions by similarity. We show the interest of our approach by applying it to a European Parliament dataset.     

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.     

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.     

k-means-based algorithm for blockmodeling linked networks

The paper presents a k-means-based algorithm for blockmodeling linked networks where linked networks are defined as a collection of one-mode and two-mode networks in which units from different one-mode networks are connected through two-mode networks. The reason for this is that a faster algorithm is needed for blockmodeling linked networks that can better scale to larger networks. Examples of linked networks include multilevel networks, dynamic networks, dynamic multilevel networks, and meta-networks. Generalized blockmodeling has been developed for linked/multilevel networks, yet the generalized blockmodeling approach is too slow for analyzing larger networks. Therefore, the flexibility of generalized blockmodeling is sacrificed for the speed of k-means-based approaches, thus allowing the analysis of larger networks. The presented algorithm is based on the two-mode k-means (or KL-means) algorithm for two-mode networks or matrices. As a side product, an algorithm for one-mode blockmodeling of one-mode networks is presented. The algorithm’s use on a dynamic multilevel network with more than 400 units is presented. A situation study is also conducted which shows that k-means based algorithms are superior to relocation algorithm-based methods for larger networks (e.g. larger than 800 units) and never much worse.     

A study of sign adjustment in weighted signed networks

We analyse the adjustment of networks comprising of weighted positive (P) and negative (N) symmetric relations under the impact of various balancing rules. Five kinds of rules are studied: (1) a local minimal edge adjustment which is a special case of, (2) a local pressure based rule, (3) a local sign based rule, (4) a global rule and (5) rules varying on a local to global dimension. The convergence and convergent proportions of different 3-cycles and, thus the impact upon β(3) balance, under the different kinds of adjustment rule are studied both analytically and through simulation. The effects of network size (n), density (d) and the initial proportion of positive edges (α₀) upon the convergence of 3-cycles and, thus, balance and the eventual implications for the process of group formation are explored.     

Approaches to blockmodeling dynamic networks: A Monte Carlo simulation study

Blockmodeling refers to a variety of statistical methods for reducing and simplifying large and complex networks. While methods for blockmodeling networks observed at one time point are well established, it is only recently that researchers have proposed several methods for analysing dynamic networks (i.e., networks observed at multiple time points). The considered approaches are based on k-means or stochastic blockmodeling, with different ways being used to model time dependency among time points. Their novelty means they have yet to be extensively compared and evaluated and the paper therefore aims to compare and evaluate them using Monte Carlo simulations. Different network characteristics are considered, including whether tie formation is random or governed by local network mechanisms. The results show the Dynamic Stochastic Blockmodel (Matias and Miele 2017) performs best if the blockmodel does not change; otherwise, the Stochastic Blockmodel for Multipartite Networks (Bar-Hen et al. 2020) does.     

Beauty and social capital: Being attractive shapes social networks

It is a fact of life that being beautiful is advantageous (Hamermesh, 2011). Whether we consider incomes or the marriage market, the more attractive one is, the better one does. Drawing on psychological research that explains why beauty pays, we hypothesize that more attractive people will exploit social network opportunities differently than less attractive people and, consequently, their networks will comprise more beneficial features. As predicted, results of an experiment showed that more attractive people were more likely to select for themselves more profitable broker positions in networks relative to other positions and relative to less attractive people. Relying on network data supplied by young professionals, in a follow-up study we found that the networks of more attractive people were relatively less dense, as the findings of Study 1 would imply. We discuss the implications for our work as well as highlight the need for further research into an understudied, but potentially influential brokerage contingency factor—physical appeal.     

Fast clustering for signed graphs based on random walk gap

Signed graphs are often used as models for social media mining, social networks analysis and nature language processing. In this paper, we study clustering algorithms for signed graphs that can be scaled for use in large-scale signed networks. A proposed mechanism, called a random walk gap (RWG), is used to extract more cluster structure information. RWG uses two types of random walks on signed graphs. The first considers positive edges only. The second takes negative edges into account. Three types of edges in signed graphs are identified and their different characteristics in terms of transition probability changes are determined for the two types of random walk graphs. Different characteristics contain different information about cluster structure and a RWG matrix is used to reflect the differences. The RWG matrix is used to adjust the weights of edges in signed graphs. This is the first study to perform a random walk on negative edges. A fast clustering for signed graphs (FCSG) algorithm is then proposed. This FCSG is compared with existing methods. The computational times for different algorithms are measured. The experiments show that the proposed FCSG algorithm gives better results than existing algorithms based on the performance criteria of imbalance and modularity.     

Mixed integer programming formulations for clustering problems related to structural balance

In this work, we study graph clustering problems associated with structural balance. One of these problems is known in computer science literature as the correlation-clustering (CC) problem and another (RCC) can be viewed as its relaxed version. The solution of CC and RCC problems has been previously used in the literature as tools for the evaluation of structural balance in a social network. Our aim is to solve these problems to optimality. We describe integer linear programming formulations for these problems which includes the first mathematical formulation for the RCC problem. We also discuss alternative models for the relaxed structural balance and the solution of clustering problems associated with these new models. Numerical experiments are carried out with each formulation on a set of benchmark instances available in the literature.     

Extended structures of mediation: Re-examining brokerage in dynamic networks

In this paper we revisit the concept of brokerage in social networks. We elaborate on the concept of brokerage as a process, identifying three distinct classes of brokerage behavior. Based on this process model, we develop a framework for measuring brokerage opportunities in dynamic relational data. Using data on emergent inter-organizational collaborations, we employ the dynamic brokerage framework to examine the relationship between organizational attributes and coordination in the evolving network. Comparing the findings of our process-based definition with traditional, static approaches, we identify important dimensions of organizational action that would be missed by the latter approach.     

Personal networks typologies: A structural approach

Building typologies allows to compare networks on multiple dimensions, and to approach a generalization grounded on empirical data. In this article, we present a typology of personal networks only based on indicators related to the structure of relations between alters. It is designed from very detailed data on young French people who were involved in a longitudinal study. Our typology mobilizes a small number of indicators to discriminate the types that compose it. In so doing, we intend to make it applicable to various surveys.     

Biased networks and social structure theorems

It is shown that the part of Peter Blau's theory of social structure bearing on heterogeneity can be imbedded within the framework of biased networks, thereby clarifying conceptual aspects of the theory as well as providing a mathematical proof of the most central heterogeneity theorem for a class of networks. The key step is the postulation of a mathematical concept of salience, called an ‘inbreeding bias’ in prior work, which corresponds to Blau's fundamental axiom. In addition, there are derivations and discussions bearing on related topics in the analysis of social structure.     

The co-evolution of gossip and friendship in workplace social networks

This study investigates the co-evolution of friendship and gossip in organizations. Two contradicting perspectives are tested. The social capital perspective predicts that friendship causes gossip between employees, defined as informal evaluative talking about absent colleagues. The evolutionary perspective reverses this causality claiming that gossiping facilitates friendship. The data comprises of three observations of a complete organizational network, allowing longitudinal social network analyses. Gossip and friendship are modeled as both explanatory and outcome networks with RSiena. Results support the evolutionary perspective in that gossip between two individuals increases the likelihood of their future friendship formation. However, individuals with disproportionately high gossip activity have fewer friends in the network, suggesting that the use of gossiping to attract friends has a limit.     

Gender,rank, and social networks on an enterprise social media platform

In this paper, we harness server-side data—540,000 messages generated by 2085 users on TamTamy, an Enterprise Social Media (ESM) platform—to examine how gender and rank shaped “homophily” (the tendency to connect with similar others) and centrality in an ESM network. Drawing on the logic of “distinctiveness theory,” which argues that the numeric rarity of a category in a given setting promotes the use of that category as a basis for connecting with others, we hypothesized and found: (a) the tendency to connect with same-gender others was stronger among women than among men; (b) the tendency to connect with same-rank others was stronger among high-ranking employees than among low-ranking employees; (c) for high-ranking men, rank was more important than gender as a basis for connecting with others; and (d) for low-ranking women, gender was more important than rank as a basis for connecting with others. We also found that whereas higher ranking individuals were more likely to be in central (bridging) positions in the overall network, gender was unrelated to network centrality. Our study suggests that the affordances of ESM for open and distributed communications notwithstanding, the social networks that emerge on ESM platforms may reinforce social stratification on some dimensions while diminishing it on others.     

Power and the perception of social networks

Previous work has led to divergent conclusions about how power affects the accuracy of network perceptions in groups and organizations. This paper develops and tests an argument linking higher power to less accurate network perception. Results from the first experiment showed that, relative to participants primed with high power, those primed with low power had more accurate perceptions of who was tied to whom in novel networks. The second experiment demonstrated that such differences in perceptual accuracy do not emerge for non-social relations.