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.     

Partitioning signed social networks

Structural balance theory has proven useful for delineating the blockmodel structure of signed social networks. Even so, most of the observed signed networks are not perfectly balanced. One possibility for this is that in examining the dynamics underlying the generation of signed social networks, insufficient attention has been given to other processes and features of signed networks. These include: actors who have positive ties to pairs of actors linked by a negative relation or who belong to two mutually hostile subgroups; some actors that are viewed positively across the network despite the presence of negative ties and subsets of actors with negative ties towards each other. We suggest that instead viewing these situations as violations of structural balance, they can be seen as belonging to other relevant processes we call mediation, differential popularity and internal subgroup hostility. Formalizing these ideas leads to the relaxed structural balance blockmodel as a proper generalization of structural balance blockmodels. Some formal properties concerning the relation between these two models are presented along with the properties of the fitting method proposed for the new blockmodel type. The new method is applied to four empirical data sets where improved fits with more nuanced interpretations are obtained.     

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.     

Acyclic triplets and social structure in complete signed digraphs

This report is a study of the relationship between certain systems of signed acyclic triplets representing relationships among three actors and the properties of the graphs which they generate. It is a method of investigating macro-structure based on micro-structural properties. The motivation stems from the work of Cartwright and Harary, Davis, Leinhardt and Holland on affective ties, which we generalize. After showing the connections between our approach and theirs, we develop some new models that go beyond affect and positive sentiment.     

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.     

Testing transitivity in graphs

The situation is considered whether a graph can be assumed to have been generated by a random model capturing more transitivity than a simple uniform model. Three different test quantities based on induced triad counts and local densities are used. A simulation study is made in order to estimate critical values of the tests for different significance levels. The powers of the tests are estimated against the Bernoulli triangle model, a simple random graph model in which the clustering and transitivity is higher than in the uniform model. The test based on the proportion of transitive triads has the highest power in most cases, but the test based on density difference (the difference between mean local density and overall graph density) is more powerful against models with high transitivity. The tests are applied to a large set of school class sociograms. In this situation, uniform randomness is rejected in favor of transitivity most frequently when the test based on the proportion of transitive triads out of the non-vacuously transitive triads is used. It is concluded that this test, which also performed reasonably well when applied to random data, is the best at detecting transitivity. Although the Bernoulli triangle model fits to the empirical data set better than the uniform model, there are fewer truly intransitive triads in the data than could be expected under either of the models.     

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.     

Testing centralization in random graphs

Centrality is an important concept in social network analysis which involves identification of important or prominent actors. Three common definitions of centrality are degree centrality, closeness centrality and betwenness centrality which yield actor indices. By aggregating these actor indices of centrality across actors, we obtain a single group-level index of centralization. In this paper, we consider the problem of testing whether the observed data is likely to have come from a particular kind of centralized structure of a given size, edge probability and extent of centralization. Eight different group-level indices of centralization are used as test statistics of graph centralization. As our graph model, we assume a general blockmodel which allows a rich probabilistic structure. By carrying out a simulation study the performance of the tests is evaluated by comparing their power functions. The results imply that two tests based on degree and four tests based on closeness have high power. In addition, critical values of the tests are modeled conditional on graph parameters via a linear regression model. An application is illustrated with analysis on a real data set.     

The sign of affection: Balance-theoretic models and incomplete signed digraphs

The initial structural models based on balance theory (structural balance and clusterability) dealt with incomplete signed digraphs. However, newer models (ranked clusters, transitivity, hierarchical M̄-cliques) apply only to zero-one matrices representing either unsigned digraphs or complete signed digraphs. Since empirical networks of affective relations are signed but seldom complete — actors may have neutral feelings towards alters or affections may be unknown to the researcher — the latter models must be redefined if affective relations are to be analysed. It was found that each balance-theoretic model is characterised by a particular type of semicycle or path. Counts of the types of semicycles and paths suffice to identify the models. This approach is more general than triadic analysis because it handles complete as well as incomplete signed digraphs.     

Some reflections on song theory,signed song and traditional song

In this article I will aim to present results of research which deals with the French word ‘chanson’ and song theory. My observations will be conducted within a metalinguistic and a linguistic corpora. My corpora was largely constituted by works published in France in addition to other countries in Europe. The study of European dictionaries has shown me how important the French song culture has become in German dictionaries (in which chansonnier and chanson de geste sometimes appear) and in Italian dictionaries (in which chansonnier as a synomym of cantaautore appears). This presentation contains some diachronical and theoretical observations. The research appears to be the first significant research conducted about the vocabulary of song in French. This will finally lead us to present the theoretical vocabulary that we have created to study song phenomena.     

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.     

The Discourse of Balance: Balance as Metaphor and Ideology

La combination du travail payé et la maternité est difficile parce que les institutions sociales sont basées sur la supposition que les deux sont toujous mutuellement exclusifs. Les mères qui travaillent gèrent la tension entre le travail et la maternité chaque jour, et quand elles le font, elles établissent des nouveaux modèles sociaux. Cette recherche présente les résultats d'une étude de 21 mères qui travaillent de la classe moyenne et soutient qu'elles ont été incapables de challenger l'organisation punitive du travail et de la maternité. Ces mères utilisent la métaphore de l’“équilibre” pour décrire comment elles gèrent la tension. Cependant, leurs récits des difficultés de gérer la maternité lorsque les méres travaillent décrit une autre histoire. En fait, l’“équilibre” est une idéologie qui fonctionne afin d'obscurcir la contradiction entre le travail et la maternité. Combining paid work and motherhood is difficult because social institutions are still based on the assumption that these are mutually exclusive. Working mothers manage the tension between work and motherhood daily, and as they do, they establish new social patterns. This paper reports on the findings of a study of 21 middle‐class working mothers and argues that they have been unable to challenge the punitive organization of work and motherhood. These mothers use the metaphor of “balance” to describe how they manage the tension. However, their narratives of the difficulties of managing working motherhood tell a different story. In fact, “balance” is an ideology, which functions to obscure the contradiction between work and motherhood.     

埃及对外政策中的平衡战略

50年代初至70年代末,埃及的对外政策受制于两极格局,其外交活动基本上是以美苏为轴心展开的,穆巴拉克任总统后,对世界格局形成了新的见解,认为世界应该建立在多极力量之上.由此,穆巴拉克总统重新审视了埃及的外交政策,提出了外交平衡战略思想,即以我为主,发展多边关系,推动经济建设.这些年来的实践证明,埃及通过频繁、多方位的外交活动,既扩大了埃及的国际影响,提高了埃及地区大国的地位,也推动了埃及经济的迅速发展.     

Internal cohesion of ls sets in graphs

Let G be a finite connected graph. A set of vertices H ? V(G) is called a LS set if for every proper subset K ? H, there are more edges linking K to H ? K than there are linking K to V(G)-H. Since “cliques” in social networks have usually been seen informally as sets of individuals more closely tied to each other than to outsiders, LS sets provide a natural realization of the “clique” concept. In this paper, it is shown that LS sets in social networks have cohesive properties that make them even more useful for empirical analyses. In particular, subgraphs induced by LS subsets remain connected even after several edges have been removed. Results bounding the number of edges that can be so removed are used to get an upper bound for the diameter of subgraphs induced by LS subsets.     

Elitism and stochastic dominance

Stochastic dominance has been typically used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in this article the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) comparisons of affluence as opposed to poverty between countries.     

国家资产负债表研究

企业资产负债表是反映企业在某一特定日期全部资产、负债和所有者权益情况的静态会计报表,是企业中长期决策的根本依据,也是甄别企业财务状态的主要信息来源之一。我国的企业资产负债表编制已较成熟,但国家资产负债表编制相对滞后。政府在实施经济政策、制定经济规划时,缺少必要的财务决策依据。同时,政府经常对经济实施＂宏观调控＂,且拥有相当大的财政支配权、裁定权,但对政府缺少必要的财务约束机制。因此,研究国家资产负债表对我国现有体制下的经济建设与社会发展尤为重要。重点应研究：资产、负债和所有者权益的组成;国家资产负债表的编制方法;国家资产负债表的应用;国家资产负债表对地方政府的影响等。