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Computation
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Computational Social Science and Complex Systems
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Computational Social Science and Complex Systems

A special issue of Computation (ISSN 2079-3197). This special issue belongs to the section "Computational Engineering".

Deadline for manuscript submissions: 30 April 2024 | Viewed by 26770

Special Issue Editors

Dr. Minzhang Zheng

E-Mail Website
Guest Editor
Physics Department, George Washington University, Washington, DC 20052, USA
Interests: complex systems; network science; systems biology and computational social science
Dr. Pedro D. Manrique

E-Mail Website
Guest Editor
Physics Department, George Washington University, Washington, DC 20056, USA
Interests: complex systems; non-equilibrium physics; networks; biophysics; math modeling
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Social and technological revolutions, such as the internet and social media, have profoundly transformed the way humans interact with one another, leading to the development of disciplines such as computing and information technology. We now have access to previously unimaginable amounts of information and high-resolution dynamical data that other sciences can only imagine. From the movements of individuals to the continuous activity taking place in social networks, a challenge for the social and computational sciences is to extract relevant information from these massive amounts of data and unravel the mechanisms that drive its complex dynamics. Computational social science is an emerging discipline in charge of developing and applying computational methods to deal with complex, large-scale, human behavioral data. This interdisciplinary field has attracted great interest among not only social scientists, but also among computer scientists and statistical physicists alike.

This Special Issue is devoted to presenting recent developments in the computational and mathematical techniques of data extraction and visualization, analysis, and modeling of complex social structures, and bringing a new understanding to the field of computational social sciences. The topics of this Special Issue include but are not limited to:

  • Computer simulation applications in social systems;
  • Social media and social network analysis;
  • Application of big data and artificial intelligence in social science;
  • Social math and modeling;
  • Progress of complex systems;
  • Computational modeling of cognition;
  • Ethics and computational social science.

Dr. Minzhang Zheng
Dr. Pedro D. Manrique
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computational social science
  • complex systems
  • big data
  • social networks
  • machine learning
  • natural language processing.

Published Papers (13 papers)

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Research

35 pages, 17424 KiB  
Article
Detecting Overlapping Communities Based on Influence-Spreading Matrix and Local Maxima of a Quality Function
by Vesa Kuikka
Computation 2024, 12(4), 85; https://doi.org/10.3390/computation12040085 - 22 Apr 2024
Viewed by 247
Abstract
Community detection is a widely studied topic in network structure analysis. We propose a community detection method based on the search for the local maxima of an objective function. This objective function reflects the quality of candidate communities in the network structure. The [...] Read more.
Community detection is a widely studied topic in network structure analysis. We propose a community detection method based on the search for the local maxima of an objective function. This objective function reflects the quality of candidate communities in the network structure. The objective function can be constructed from a probability matrix that describes interactions in a network. Different models, such as network structure models and network flow models, can be used to build the probability matrix, and it acts as a link between network models and community detection models. In our influence-spreading model, the probability matrix is called an influence-spreading matrix, which describes the directed influence between all pairs of nodes in the network. By using the local maxima of an objective function, our method can standardise and help in comparing different definitions and approaches of community detection. Our proposed approach can detect overlapping and hierarchical communities and their building blocks within a network. To compare different structures in the network, we define a cohesion measure. The objective function can be expressed as a sum of these cohesion measures. We also discuss the probability of community formation to analyse a different aspect of group behaviour in a network. It is essential to recognise that this concept is separate from the notion of community cohesion, which emphasises the need for varying objective functions in different applications. Furthermore, we demonstrate that normalising objective functions by the size of detected communities can alter their rankings. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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25 pages, 924 KiB  
Article
Graph-Based Interpretability for Fake News Detection through Topic- and Propagation-Aware Visualization
by Kayato Soga, Soh Yoshida and Mitsuji Muneyasu
Computation 2024, 12(4), 82; https://doi.org/10.3390/computation12040082 - 15 Apr 2024
Viewed by 455
Abstract
In the context of the increasing spread of misinformation via social network services, in this study, we addressed the critical challenge of detecting and explaining the spread of fake news. Early detection methods focused on content analysis, whereas recent approaches have exploited the [...] Read more.
In the context of the increasing spread of misinformation via social network services, in this study, we addressed the critical challenge of detecting and explaining the spread of fake news. Early detection methods focused on content analysis, whereas recent approaches have exploited the distinctive propagation patterns of fake news to analyze network graphs of news sharing. However, these accurate methods lack accountability and provide little insight into the reasoning behind their classifications. We aimed to fill this gap by elucidating the structural differences in the spread of fake and real news, with a focus on opinion consensus within these structures. We present a novel method that improves the interpretability of graph-based propagation detectors by visualizing article topics and propagation structures using BERTopic for topic classification and analyzing the effect of topic agreement on propagation patterns. By applying this method to a real-world dataset and conducting a comprehensive case study, we not only demonstrated the effectiveness of the method in identifying characteristic propagation paths but also propose new metrics for evaluating the interpretability of the detection methods. Our results provide valuable insights into the structural behavior and patterns of news propagation, contributing to the development of more transparent and explainable fake news detection systems. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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16 pages, 3793 KiB  
Article
Method to Forecast the Presidential Election Results Based on Simulation and Machine Learning
by Luis Zuloaga-Rotta, Rubén Borja-Rosales, Mirko Jerber Rodríguez Mallma, David Mauricio and Nelson Maculan
Computation 2024, 12(3), 38; https://doi.org/10.3390/computation12030038 - 22 Feb 2024
Viewed by 1960
Abstract
The forecasting of presidential election results (PERs) is a very complex problem due to the diversity of electoral factors and the uncertainty involved. The use of a hybrid approach composed of techniques such as machine learning (ML) and Simulation in forecasting tasks is [...] Read more.
The forecasting of presidential election results (PERs) is a very complex problem due to the diversity of electoral factors and the uncertainty involved. The use of a hybrid approach composed of techniques such as machine learning (ML) and Simulation in forecasting tasks is promising because the former presents good results but requires a good balance between data quantity and quality, and the latter supplies said requirement; nonetheless, each technique has its limitations, parameters, processes, and application contexts, which should be treated as a whole to improve the results. This study proposes a systematic method to build a model to forecast the PERs with high precision, based on the factors that influence the voter’s preferences and the use of ML and Simulation techniques. The method consists of four phases, uses contextual and synthetic data, and follows a procedure that guarantees high precision in predicting the PER. The method was applied to real cases in Brazil, Uruguay, and Peru, resulting in a predictive model with 100% agreement with the actual first-round results for all cases. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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19 pages, 6917 KiB  
Article
Cooperation Dynamic through Individualistic Indirect Reciprocity Mechanism in a Multi-Dynamic Model
by Mario-Ignacio González-Silva and Ricardo-Armando González-Silva
Computation 2024, 12(2), 20; https://doi.org/10.3390/computation12020020 - 24 Jan 2024
Viewed by 1269
Abstract
This research proposes a new variant of Nowak and Sigmund’s indirect reciprocity model focused on agents’ individualism, which means that an agent strengthens its profile to the extent to which it makes a profit; this is using agent-based modeling. In addition, our model [...] Read more.
This research proposes a new variant of Nowak and Sigmund’s indirect reciprocity model focused on agents’ individualism, which means that an agent strengthens its profile to the extent to which it makes a profit; this is using agent-based modeling. In addition, our model includes environmentally related conditions such as visibility and cooperative demand and internal poses such as obstinacy. The simulation results show that cooperators appear in a more significant proportion with conditions of low reputation visibility and high cooperative demand. Still, severe defectors take advantage of this situation and exceed the cooperators’ ratio. Some events show a heterogeneous society only with conditions of high obstinacy and cooperative demand. In general, the simulations show diverse scenarios, including centralized, polarized, and mixed societies. Simulation results show no healthy cooperation in indirect reciprocity due to individualism. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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21 pages, 3450 KiB  
Article
Building Political Hashtag Communities: A Multiplex Network Analysis of U.S. Senators on Twitter during the 2022 Midterm Elections
by Yunus Emre Orhan, Harun Pirim and Yusuf Akbulut
Computation 2023, 11(12), 238; https://doi.org/10.3390/computation11120238 - 01 Dec 2023
Viewed by 1734
Abstract
This study examines how U.S. senators strategically used hashtags to create political communities on Twitter during the 2022 Midterm Elections. We propose a way to model topic-based implicit interactions among Twitter users and introduce the concept of Building Political Hashtag Communities (BPHC). Using [...] Read more.
This study examines how U.S. senators strategically used hashtags to create political communities on Twitter during the 2022 Midterm Elections. We propose a way to model topic-based implicit interactions among Twitter users and introduce the concept of Building Political Hashtag Communities (BPHC). Using multiplex network analysis, we provide a comprehensive view of elites’ behavior. Through AI-driven topic modeling on real-world data, we observe that, at a general level, Democrats heavily rely on BPHC. Yet, when disaggregating the network across layers, this trend does not uniformly persist. Specifically, while Republicans engage more intensively in BPHC discussions related to immigration, Democrats heavily rely on BPHC in topics related to identity and women. However, only a select group of Democratic actors engage in BPHC for topics on labor and the environment—domains where Republicans scarcely, if at all, participate in BPHC efforts. This research contributes to the understanding of digital political communication, offering new insights into echo chamber dynamics and the role of politicians in polarization. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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18 pages, 5308 KiB  
Article
A Novel Methodology Analyzing the Influence of Micro-Stresses on Human-Centric Environments
by Nataliya Shakhovska, Roman Kaminskyy, Bohdan Khudoba, Vladyslav Mykhailyshyn and Ihor Helzhynskyi
Computation 2023, 11(11), 224; https://doi.org/10.3390/computation11110224 - 06 Nov 2023
Viewed by 1341
Abstract
This article offers experimental studies and a new methodology for analyzing the influence of micro-stresses on human operator activity in man–machine information and search interfaces. Human-centered design is a problem-solving technique that puts real people at the center of the design process. Therefore, [...] Read more.
This article offers experimental studies and a new methodology for analyzing the influence of micro-stresses on human operator activity in man–machine information and search interfaces. Human-centered design is a problem-solving technique that puts real people at the center of the design process. Therefore, mindfulness is one of the most important aspects in various fields such as medicine, industry, and decision-making. The human-operator activity model can be used to create a database of specialized test images and a computer for its implementation. The peculiarity of the tests is that they represent images of real work situations obtained as a result of texture stylization and allow the use of an appropriate search difficulty scale. A mathematical model of a person who makes a decision is built. The requirements for creating a switch to solve the given problem are discussed. This work summarizes the accumulated experience of such studies. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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20 pages, 784 KiB  
Article
Influence of Media Information Sources on Vaccine Uptake: The Full and Inconsistent Mediating Role of Vaccine Hesitancy
by Almudena Recio-Román, Manuel Recio-Menéndez and María Victoria Román-González
Computation 2023, 11(10), 208; https://doi.org/10.3390/computation11100208 - 23 Oct 2023
Viewed by 1731
Abstract
Vaccine hesitancy is a significant public health concern, with numerous studies demonstrating its negative impact on immunization rates. One factor that can influence vaccine hesitancy is media coverage of vaccination. The media is a significant source of immunization information and can significantly shape [...] Read more.
Vaccine hesitancy is a significant public health concern, with numerous studies demonstrating its negative impact on immunization rates. One factor that can influence vaccine hesitancy is media coverage of vaccination. The media is a significant source of immunization information and can significantly shape people’s attitudes and behaviors toward vaccine uptake. Media influences vaccination positively or negatively. Accurate coverage of the benefits and effectiveness of vaccination can encourage uptake, while coverage of safety concerns or misinformation may increase hesitancy. Our study investigated whether vaccine hesitancy acts as a mediator between information sources and vaccination uptake. We analyzed a cross-sectional online survey by the European Commission of 27,524 citizens from all EU member states between 15 and 29 March 2019. The study used structural equation modeling to conduct a mediation analysis, revealing that the influence of media on vaccine uptake is fully mediated by vaccine hesitancy, except for television, which depicted an inconsistent mediating role. In other words, the effect of different media on vaccine uptake is largely driven by the extent to which individuals are hesitant or resistant to vaccinating. Therefore, media outlets, governments, and public health organizations must work together to promote accurate and reliable information about vaccination and address vaccine hesitancy. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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17 pages, 2652 KiB  
Article
Incorporating Time-Series Forecasting Techniques to Predict Logistics Companies’ Staffing Needs and Order Volume
by Ahmad Alqatawna, Bilal Abu-Salih, Nadim Obeid and Muder Almiani
Computation 2023, 11(7), 141; https://doi.org/10.3390/computation11070141 - 14 Jul 2023
Cited by 5 | Viewed by 6862
Abstract
Time-series analysis is a widely used method for studying past data to make future predictions. This paper focuses on utilizing time-series analysis techniques to forecast the resource needs of logistics delivery companies, enabling them to meet their objectives and ensure sustained growth. The [...] Read more.
Time-series analysis is a widely used method for studying past data to make future predictions. This paper focuses on utilizing time-series analysis techniques to forecast the resource needs of logistics delivery companies, enabling them to meet their objectives and ensure sustained growth. The study aims to build a model that optimizes the prediction of order volume during specific time periods and determines the staffing requirements for the company. The prediction of order volume in logistics companies involves analyzing trend and seasonality components in the data. Autoregressive (AR), Autoregressive Integrated Moving Average (ARIMA), and Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) are well-established and effective in capturing these patterns, providing interpretable results. Deep-learning algorithms require more data for training, which may be limited in certain logistics scenarios. In such cases, traditional models like SARIMAX, ARIMA, and AR can still deliver reliable predictions with fewer data points. Deep-learning models like LSTM can capture complex patterns but lack interpretability, which is crucial in the logistics industry. Balancing performance and practicality, our study combined SARIMAX, ARIMA, AR, and Long Short-Term Memory (LSTM) models to provide a comprehensive analysis and insights into predicting order volume in logistics companies. A real dataset from an international shipping company, consisting of the number of orders during specific time periods, was used to generate a comprehensive time-series dataset. Additionally, new features such as holidays, off days, and sales seasons were incorporated into the dataset to assess their impact on order forecasting and workforce demands. The paper compares the performance of the four different time-series analysis methods in predicting order trends for three countries: United Arab Emirates (UAE), Kingdom of Saudi Arabia (KSA), and Kuwait (KWT), as well as across all countries. By analyzing the data and applying the SARIMAX, ARIMA, LSTM, and AR models to predict future order volume and trends, it was found that the SARIMAX model outperformed the other methods. The SARIMAX model demonstrated superior accuracy in predicting order volumes and trends in the UAE (MAPE: 0.097, RMSE: 0.134), KSA (MAPE: 0.158, RMSE: 0.199), and KWT (MAPE: 0.137, RMSE: 0.215). Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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35 pages, 5956 KiB  
Article
Social Networks in Military Powers: Network and Sentiment Analysis during the COVID-19 Pandemic
by Alberto Quilez-Robres, Marian Acero-Ferrero, Diego Delgado-Bujedo, Raquel Lozano-Blasco and Montserrat Aiger-Valles
Computation 2023, 11(6), 117; https://doi.org/10.3390/computation11060117 - 13 Jun 2023
Viewed by 1337
Abstract
The outbreak of the COVID-19 pandemic shifted socialization and information seeking to social media platforms. The armed forces of the major military powers initiated civil support operations to combat the invisible and common enemy. The aim of this study is to analyze the [...] Read more.
The outbreak of the COVID-19 pandemic shifted socialization and information seeking to social media platforms. The armed forces of the major military powers initiated civil support operations to combat the invisible and common enemy. The aim of this study is to analyze the existence of differential behavior in the corporate profiles of the major military powers on Twitter, Instagram, and Facebook during the COVID-19 pandemic. The principles of social network analysis were followed, along with sentiment analysis, to study web positioning and the emotional content of the posts (N = 25,328). The principles of data mining were applied to process the KPIs (Fanpage Karma), and an artificial intelligence (meaning cloud) sentiment analysis was applied to study the emotionality of the publications. The analysis was carried out using the IBM SPSS Statistics 25 statistical software. Subsequently, a qualitative content analysis was carried out using frequency graphs or word clouds (the application “nubedepalabras” used in English). Significant differences were found between the behavior on social media and the organizational and communicative culture of the nations. It is highlighted that some nations present different preferences from the main communicative strategy developed by their armed forces. Corporate communication of the major military powers should consider the emotional nature of their posts to align with the preferences of their population. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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19 pages, 6789 KiB  
Article
Opinion Formation on Social Networks—The Effects of Recurrent and Circular Influence
by Vesa Kuikka
Computation 2023, 11(5), 103; https://doi.org/10.3390/computation11050103 - 22 May 2023
Cited by 2 | Viewed by 1471
Abstract
We present a generalised complex contagion model for describing behaviour and opinion spreading on social networks. Recurrent interactions between adjacent nodes and circular influence in loops in the network structure enable the modelling of influence spreading on the network scale. We have presented [...] Read more.
We present a generalised complex contagion model for describing behaviour and opinion spreading on social networks. Recurrent interactions between adjacent nodes and circular influence in loops in the network structure enable the modelling of influence spreading on the network scale. We have presented details of the model in our earlier studies. Here, we focus on the interpretation of the model and discuss its features by using conventional concepts in the literature. In addition, we discuss how the model can be extended to account for specific social phenomena in social networks. We demonstrate the differences between the results of our model and a simple contagion model. Results are provided for a small social network and a larger collaboration network. As an application of the model, we present a method for profiling individuals based on their out-centrality, in-centrality, and betweenness values in the social network structure. These measures have been defined consistently with our spreading model based on an influence spreading matrix. The influence spreading matrix captures the directed spreading probabilities between all node pairs in the network structure. Our results show that recurrent and circular influence has considerable effects on node centrality values and spreading probabilities in the network structure. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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11 pages, 410 KiB  
Article
Social Learning and the Exploration-Exploitation Tradeoff
by Brian Mintz and Feng Fu
Computation 2023, 11(5), 101; https://doi.org/10.3390/computation11050101 - 18 May 2023
Viewed by 1113
Abstract
Cultures around the world show varying levels of conservatism. While maintaining traditional ideas prevents wrong ones from being embraced, it also slows or prevents adaptation to new times. Without exploration there can be no improvement, but often this effort is wasted as it [...] Read more.
Cultures around the world show varying levels of conservatism. While maintaining traditional ideas prevents wrong ones from being embraced, it also slows or prevents adaptation to new times. Without exploration there can be no improvement, but often this effort is wasted as it fails to produce better results, making it better to exploit the best known option. This tension is known as the exploration/exploitation issue, and it occurs at the individual and group levels, whenever decisions are made. As such, it is has been investigated across many disciplines. We extend previous work by approximating a continuum of traits under local exploration, employing the method of adaptive dynamics, and studying multiple fitness functions. In this work, we ask how nature would solve the exploration/exploitation issue, by allowing natural selection to operate on an exploration parameter in a variety of contexts, thinking of exploration as mutation in a trait space with a varying fitness function. Specifically, we study how exploration rates evolve by applying adaptive dynamics to the replicator-mutator equation, under two types of fitness functions. For the first, payoffs are accrued from playing a two-player, two-action symmetric game, we consider representatives of all games in this class, including the Prisoner’s Dilemma, Hawk-Dove, and Stag Hunt games, finding exploration rates often evolve downwards, but can also undergo neutral selection as well depending on the games parameters or initial conditions. Second, we study time dependent fitness with a function having a single oscillating peak. By increasing the period, we see a jump in the optimal exploration rate, which then decreases towards zero as the frequency of environmental change increases. These results establish several possible evolutionary scenarios for exploration rates, providing insight into many applications, including why we can see such diversity in rates of cultural change. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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11 pages, 297 KiB  
Article
Problem Solving and Budget Allocation of SMEs: Application of NCA Approach
by Parisa Bouzari, Balázs Gyenge, Pejman Ebrahimi and Mária Fekete-Farkas
Computation 2023, 11(3), 48; https://doi.org/10.3390/computation11030048 - 28 Feb 2023
Cited by 1 | Viewed by 3647
Abstract
In order to achieve a specific result, a firm’s problem-solving activities can be thought of as a process that combines physical and cognitive actions. Its internal organization determines how information inputs are distributed among different task units and, as a result, how the [...] Read more.
In order to achieve a specific result, a firm’s problem-solving activities can be thought of as a process that combines physical and cognitive actions. Its internal organization determines how information inputs are distributed among different task units and, as a result, how the cognitive workload is distributed. We tested a case study related to Iranian small and medium enterprises (SMEs). We used NCA analysis as a creative and state-of-the-art method with the help of R software to evaluate data. According to the findings, six prerequisites must be met in order to achieve a 50% level of efficient performance: innovation at a minimum of 22.7%, CSR at a minimum of 30.4%, IT investment at a minimum of 56.7%, SMM at a minimum of 38.3%, product differentiation at a minimum of 11.7%, and CRM at a minimum of 38.3%. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
20 pages, 7600 KiB  
Article
Computational Triangulation in Mathematics Teacher Education
by Sergei Abramovich
Computation 2023, 11(2), 31; https://doi.org/10.3390/computation11020031 - 10 Feb 2023
Cited by 2 | Viewed by 1628
Abstract
The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is [...] Read more.
The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser used as background for (what is called in the paper) computational triangulation in the context of four digital tools. Computational problem solving and problem formulating are presented as two sides of the same coin. By revealing the hidden mathematics of Fibonacci numbers included in the Brain Teaser, the paper discusses the role of computational thinking in the use of the well-ordering principle, the generating function method, digital fabrication, difference equations, and continued fractions in the development of computational algorithms. These algorithms eventually lead to a generalized Golden Ratio in the form of a string of numbers independently generated by digital tools used in the paper. Full article
(This article belongs to the Special Issue Computational Social Science and Complex Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Multiplex Network Analysis of Inter-party Relationships
Authors: Harun Pirim; Yunus Orhan; Yusuf Akbulut
Affiliation: North Dakota State University, Fargo, United States
Abstract: In polarized societies, inter-party interactions between candidates can often lead to conflicts and toxic interactions. However, little is known about the mechanisms of interactions between candidates. Here we study inter-party interactions across 6000 US 2022 midterm election candidates on Twitter, examining (a) which topics spark the most heated debates within candidate networks on Twitter and (b) how toxicity level/gender/race of candidates moderate the inter-party network interactions. We expect that (1) most of the links originating within either the Democrat or Republican candidates could stay within their party communities; (2) this pattern could be more evident in the retweet network, but less in the mention network; (3) inter-party interactions could be more frequent at the district-level; and (4) polarization around specific policy issues (i.e., gun ownership, abortion, LGBT) could be more relevant to explain the inter-party network. We will deploy multiplex network analysis to address these questions and derive new hypotheses. Multiplex network analysis represents distinct relationships at each layer. We will select at least five hashtags to create at least five layers of the multiplex network. The layers will be compared in terms of network metrics such as centrality, average path length, density, and clustering coefficient. Community detection will be applied to see how the candidates are clustered, considering all layers of relations. To elucidate toxicity, gender, and race relationships three layers of multiplex network will be generated. The layers will be compared, and the multiplex network will be clustered to reveal bipartisan relationships. Another multiplex network will be based on retweet and mentions networks. This network will be analyzed to see if there are party level vs. district level distinctions. Our substantive finding could suggest that using less toxic language could be a protective factor that enhances inter-party network effectiveness.

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