Generalized Blockmodeling of Multi-Valued Networks

This research presents an extension to generalized blockmodeling where there are more than two types of objects to be clustered based on valued network data. We use the ideas in homogeneity blockmodeling to develop an optimization model to perform the clustering of the objects and the resulting partitioning of the ties so as to minimize the inconsistency of an empirical block with an ideal block. The ideal block types used in this modeling are null (all zeros), complete (all ones) and valued. Two case studies are presented: the Southern Women dataset and a larger example using a subset of the IMDb movie dataset

A Network Analysis of Social Balance in Conflict in the Maghreb

This work offers the U.S. military and national security structure a methodology to analyze tension within signed networks based on social balance theory, presents a process to partition a signed network to identify likely subsets within the network, and pinpoints unique actors and relationships based on the structure of the network. Relationships identified to cause increased tension within the network are discovered and analyzed. Identifying this tension provides analysts with insight into the complexities of the network and potential relationships to target to stabilize or destabilize a network. Two Social Network Analysis models have been developed analyzing the relationships of key actors associated with the 2012-2013 conflict in Northern Mali. Relations between the terrorist group Al-Qaida in the Islamic Maghreb (AQIM), several Tuareg organizations, the Malian government and other key actors are assessed, both prior to and immediately following French and other international forces involvement beginning in January 2013. The potential effectiveness of the developed methodology is demonstrated, through the Mali example, in the identification of a specific relationship between two organizations as being under tension to change; subsequently one of the organizations split, reducing the tension and irreversibly changing the network

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 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

Generalized Blockmodeling with Pajek

Abstract One goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily. Batagelj, Doreian, and Ferligoj developed a generalized approach to blockmodeling and methods where a set of observed relations are fitted to a pre-specified blockmodel. In the paper this generalized blockmodeling approach as implemented in program Pajek is described. An overview of the blockmodeling procedures in Pajek is given and is illustrated by some examples

Animating the development of Social Networks over time using a dynamic extension of multidimensional scaling

The animation of network visualizations poses technical and theoretical challenges. Rather stable patterns are required before the mental map enables a user to make inferences over time. In order to enhance stability, we developed an extension of stress-minimization with developments over time. This dynamic layouter is no longer based on linear interpolation between independent static visualizations, but change over time is used as a parameter in the optimization. Because of our focus on structural change versus stability the attention is shifted from the relational graph to the latent eigenvectors of matrices. The approach is illustrated with animations for the journal citation environments of Social Networks, the (co-)author networks in the carrying community of this journal, and the topical development using relations among its title words. Our results are also compared with animations based on PajekToSVGAnim and SoNIA

Innovation Clusters in Technological Systems: A Network Analysis of 15 OECD Countries for the Middle '90s

The paper aims at investigating how innovations cluster in different technological systems (TSs) when their “techno-economic", rather than “territorial" space is considered. Innovation clusters of economic sectors are identified by applying network analysis to the intersectoral R&D flows matrices of 15 OECD countries in the middle '90s. Different clusterization models are first tested in order to detect the way sectors group on the basis of the embodied R&D flows they exchange. Actual clusters are then mapped in the different TSs by looking for intersectoral relationships which can be qualified to constitute “reduced-TSs" (ReTSs). In all the 15 TSs investigated the technoeconomic space appears organized in hierarchies, along which its constitutive sectors group into clusters with different density and composition. Once ReTSs are looked for, the 15 TSs display highly heterogeneous structures, but with some interesting similarity on the basis of which different clusters of TSs can be identified in turn.Innovation clusters; technological systems; R&D expenditure; embodied innovation flows

An Algorithm and Metric for Network Decomposition from Similarity Matrices: Application to Positional Analyses

We present an algorithm for decomposing a social network into an optimal number of structurally equivalent classes. The k-means method is used to determine the best decomposition of the social network for various numbers of subgroups. The best number of subgroups into which to decompose a network is determined by minimizing the intra-cluster variance of similarity subject to the constraint that the improvement in going to more subgroups is better than a random network would achieve. We also describe a decomposability metric that assesses how closely the derived decomposition approaches an ideal network having only structurally equivalent classes. Three well known network data sets were used to demonstrate the algorithm and decomposability metric. These demonstrations indicate the utility of the approach and suggest how it can be used in a complementary way to the Generalized Blockmodeling

Interbank tiering and money center banks

This paper provides evidence that interbank markets are tiered rather than flat, in the sense that most banks do not lend to each other directly but through money center banks acting as intermediaries. We capture the concept of tiering by developing a core-periphery model, and devise a procedure for tting the model to real-world networks. Using Bundesbank data on bilateral interbank exposures among 1800 banks, we find strong evidence of tiering in the German banking system. Econometrically, bank-specific features, such as balance sheet size, predict how banks position themselves in the interbank market. This link provides a promising avenue for understanding the formation of financial networks.Interbank market ; Banks and banking, Central - Germany