Detecting coalitions by optimally partitioning signed networks of political collaboration

Unpacking polarization: Antagonism and alignment in signed networks of online interaction

Political conflict is an essential element of democratic systems, but can also threaten their existence if it becomes too intense. This happens particularly when most political issues become aligned along the same major fault line, splitting society into two antagonistic camps. In the 20th century, major fault lines were formed by structural conflicts, like owners vs. workers, center vs. periphery, etc. But these classical cleavages have since lost their explanatory power. Instead of theorizing new cleavages, we present the FAULTANA (FAULT-line Alignment Network Analysis) pipeline, a computational method to uncover major fault lines in data of signed online interactions. Our method makes it possible to quantify the degree of antagonism prevalent in different online debates, as well as how aligned each debate is to the major fault line. This makes it possible to identify the wedge issues driving polarization, characterized by both intense antagonism and alignment. We apply our approach to large-scale data sets of Birdwatch, a US-based Twitter fact-checking community and the discussion forums of DerStandard, an Austrian online newspaper. We find that both online communities are divided into two large groups and that their separation follows political identities and topics. In addition, for DerStandard, we pinpoint issues that reinforce societal fault lines and thus drive polarization. We also identify issues that trigger online conflict without strictly aligning with those dividing lines (e.g. COVID-19). Our methods allow us to construct a time-resolved picture of affective polarization that shows the separate contributions of cohesiveness and divisiveness to the dynamics of alignment during contentious elections and events.

An evaluation tool for backbone extraction techniques in weighted complex networks

Networks are essential for analyzing complex systems. However, their growing size necessitates backbone extraction techniques aimed at reducing their size while retaining critical features. In practice, selecting, implementing, and evaluating the most suitable backbone extraction method may be challenging. This paper introduces netbone, a Python package designed for assessing the performance of backbone extraction techniques in weighted networks. Its comparison framework is the standout feature of netbone. Indeed, the tool incorporates state-of-the-art backbone extraction techniques. Furthermore, it provides a comprehensive suite of evaluation metrics allowing users to evaluate different backbones techniques. We illustrate the flexibility and effectiveness of netbone through the US air transportation network analysis. We compare the performance of different backbone extraction techniques using the evaluation metrics. We also show how users can integrate a new backbone extraction method into the comparison framework. netbone is publicly available as an open-source tool, ensuring its accessibility to researchers and practitioners. Promoting standardized evaluation practices contributes to the advancement of backbone extraction techniques and fosters reproducibility and comparability in research efforts. We anticipate that netbone will serve as a valuable resource for researchers and practitioners enabling them to make informed decisions when selecting backbone extraction techniques to gain insights into the structural and functional properties of complex systems.

Modified Heider balance on Erdös-Rényi networks

The lack of signed random networks in standard balance studies has prompted us to extend the Hamiltonian of the standard balance model. Random networks with tunable parameters are suitable for better understanding the behavior of standard balance as an underlying dynamics. Moreover, the standard balance model in its original form does not allow preserving tensed triads in the network. Therefore, the thermal behavior of the balance model has been investigated on a fully connected signed network recently. It has been shown that the model undergoes an abrupt phase transition with temperature. Considering these two issues, we examine the thermal behavior of the structural balance model defined on Erdös-Rényi random networks within the range of their connected regime. We provide a mean-field solution for the model. We observe a first-order phase transition with temperature for a wide range of connection probabilities. We detect two transition temperatures, T_{cold} and T_{hot}, characterizing a hysteresis loop. We find that with decreasing the connection probability, both T_{cold} and T_{hot} decrease. However, the slope of decreasing T_{hot} with decreasing connection probability is larger than the slope of decreasing T_{cold}. Hence, the hysteresis region gets narrower until it disappears in a certain connection probability. We provide a phase diagram in the temperature-tie density plane to accurately observe the metastable or coexistence region behavior. Then we justify our mean-field results with a series of Monte Carlo simulations.

backbone: An R package to extract network backbones

Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges: the backbone. This paper introduces and demonstrates a substantially expanded version of the backbone package for R, which now provides methods for extracting backbones from weighted networks, weighted bipartite projections, and unweighted networks. For each type of network, fully replicable code is presented first for small toy examples, then for complete empirical examples using transportation, political, and social networks. The paper also demonstrates the implications of several issues of statistical inference that arise in backbone extraction. It concludes by briefly reviewing existing applications of backbone extraction using the backbone package, and future directions for research on network backbone extraction.

Comparing alternatives to the fixed degree sequence model for extracting the backbone of bipartite projections

Projections of bipartite or two-mode networks capture co-occurrences, and are used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to represent unipartite networks. A key challenge in analyzing such networks is determining whether an observed number of co-occurrences between two nodes is significant, and therefore whether an edge exists between them. One approach, the fixed degree sequence model (FDSM), evaluates the significance of an edge's weight by comparison to a null model in which the degree sequences of the original bipartite network are fixed. Although the FDSM is an intuitive null model, it is computationally expensive because it requires Monte Carlo simulation to estimate each edge's p value, and therefore is impractical for large projections. In this paper, we explore four potential alternatives to FDSM: fixed fill model, fixed row model, fixed column model, and stochastic degree sequence model (SDSM). We compare these models to FDSM in terms of accuracy, speed, statistical power, similarity, and ability to recover known communities. We find that the computationally-fast SDSM offers a statistically conservative but close approximation of the computationally-impractical FDSM under a wide range of conditions, and that it correctly recovers a known community structure even when the signal is weak. Therefore, although each backbone model may have particular applications, we recommend SDSM for extracting the backbone of bipartite projections when FDSM is impractical.

Identifying hidden coalitions in the US House of Representatives by optimally partitioning signed networks based on generalized balance

In network science, identifying optimal partitions of a signed network into internally cohesive and mutually divisive clusters based on generalized balance theory is computationally challenging. We reformulate and generalize two binary linear programming models that tackle this challenge, demonstrating their practicality by applying them to partition signed networks of collaboration and opposition in the US House of Representatives. These models guarantee a globally optimal network partition and can be practically applied to signed networks containing up to 30,000 edges. In the US House context, we find that a three-cluster partition is better than a conventional two-cluster partition, where the otherwise hidden third coalition is composed of highly effective legislators who are ideologically aligned with the majority party.

Mean-field solution for critical behavior of signed networks in competitive balance theory

The competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks. In this model, two different paradigms or interests compete with each other to dominate the network's relations and impose their own values. In this paper, using the mean-field method, we examine the thermal behavior of the competitive balance model. Our results show that under a certain temperature, the symmetry between two competing interests will spontaneously break which leads to a discrete phase transition. So, starting with a heterogeneous signed network, if agents aim to decrease tension stemming from competitive balance theory, evolution ultimately chooses only one of the existing interests and stability arises where one paradigm dominates the system. The critical temperature depends linearly on the number of nodes, which is a linear dependence in the thermal balance theory as well. Finally, the results obtained through the mean-field method are verified by a series of simulations.

A signed network perspective on the government formation process in parliamentary democracies

In parliamentary democracies, government negotiations talks following a general election can sometimes be a long and laborious process. In order to explain this phenomenon, in this paper we use structural balance theory to represent a multiparty parliament as a signed network, with edge signs representing alliances and rivalries among parties. We show that the notion of frustration, which quantifies the amount of “disorder” encoded in the signed graph, correlates very well with the duration of the government negotiation talks. For the 29 European countries considered in this study, the average correlation between frustration and government negotiation talks ranges between 0.42 and 0.69, depending on what information is included in the edges of the signed network. Dynamical models of collective decision-making over signed networks with varying frustration are proposed to explain this correlation.

Backbone: An R package for extracting the backbone of bipartite projections

Bipartite projections are used in a wide range of network contexts including politics (bill co-sponsorship), genetics (gene co-expression), economics (executive board co-membership), and innovation (patent co-authorship). However, because bipartite projections are always weighted graphs, which are inherently challenging to analyze and visualize, it is often useful to examine the 'backbone,' an unweighted subgraph containing only the most significant edges. In this paper, we introduce the R package backbone for extracting the backbone of weighted bipartite projections, and use bill sponsorship data from the 114th session of the United States Senate to demonstrate its functionality.

Legislators' roll-call voting behavior increasingly corresponds to intervals in the political spectrum

Scaling techniques such as the well known NOMINATE position political actors in a low dimensional space to represent the similarity or dissimilarity of their political orientation based on roll-call voting patterns. Starting from the same kind of data we propose an alternative, discrete, representation that replaces positions (points and distances) with niches (boxes and overlap). In the one-dimensional case, this corresponds to replacing the left-to-right ordering of points on the real line with an interval order. As it turns out, this seemingly simplistic one-dimensional model is sufficient to represent the similarity of roll-call votes by U.S. senators in recent years. In a historic context, however, low dimensionality represents the exception which stands in contrast to what is suggested by scaling techniques.

Multilevel structural evaluation of signed directed social networks based on balance theory

Balance theory explains how network structural configurations relate to tension in social systems, which are commonly modeled as static undirected signed graphs. We expand this modeling approach by incorporating directionality of edges and considering three levels of analysis for balance assessment: triads, subgroups, and the whole network. For triad-level balance, we develop a new measure by utilizing semicycles that satisfy the condition of transitivity. For subgroup-level balance, we propose measures of cohesiveness (intra-group solidarity) and divisiveness (inter-group antagonism) to capture balance within and among subgroups. For network-level balance, we re-purpose the normalized line index to incorporate directionality and assess balance based on the proportion of edges whose position suits balance. Through comprehensive computational analyses, we quantify, analyze, and compare patterns of social structure in triads, subgroups, and the whole network across a range of social settings. We then apply our multilevel framework to examine balance in temporal and multilayer networks to demonstrates the generalizability of our approach. In most cases, we find relatively high balance across the three levels; providing another confirmation of balance theory. We also deliver empirical evidence for the argument that balance at different levels is not the same social phenomenon measured at different scales, but represents different properties (triadic balance, internal cohesion and external division of subgroups, and overall network polarization), and should therefore be evaluated independently from one another. We propose a comprehensive yet parsimonious approach to address this need.