Social networks and positive and negative affect

We followed 100 university students in the UK for one week, instructing them to record all face-to-face, phone and digital contacts during the day as well as their positive and negative affect. We wanted to see how positive and negative affect spread around a social network while taking into account participants’ socio-demographic data, personality, general health and gratitude scores. We focused on the participants’ connections with those in their class; excluding friends and family outside this group. The data was analysed using actor-based models implemented in SIENA. Results show differences between positive and negative affect dynamics in this environment and an influence of personality traits on the average number and rate of communication.

Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.

Social networks and occupational choice: the endogenous formation of attitudes and beliefs about tax compliance

The paper analyses the emergence of group-specific attitudes and beliefs about tax compliance when individuals interact in a social network. It develops a model in which taxpayers possess a range of individual characteristics – including attitude to risk, potential for success in self-employment, and the weight attached to the social custom for honesty – and make an occupational choice based on these characteristics. Occupations differ in the possibility for evading tax. The social network determines which taxpayers are linked, and information about auditing and compliance is transmitted at meetings between linked taxpayers. Using agent-based simulations, the analysis demonstrates how attitudes and beliefs endogenously emerge that differ across sub-groups of the population. Compliance behaviour is different across occupational groups, and this is reinforced by the development of group-specific attitudes and beliefs. Taxpayers self-select into occupations according to the degree of risk aversion, the subjective probability of audit is sustained above the objective probability, and the weight attached to the social custom differs across occupations. These factors combine to lead to compliance levels that differ across occupations.

Weighted alpha-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum alpha and alpha-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted alpha-rate domination set problem which is, to the best of our knowledge, the first such algorithm. A theoretical approximation bound based on a simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that the weights of vertices could be interpreted as the costs of getting those individuals on board for a campaign or a behaviour change intervention. The minimum weighted alpha-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least alpha percentage of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.

Interventions in social networks: impact on mood and network dynamics

Results from two studies on longitudinal friendship networks are presented, exploring the impact of a gratitude intervention on positive and negative affect dynamics in a social network. The gratitude intervention had been previously shown to increase positive affect and decrease negative affect in an individual but dynamic group effects have not been considered. In the first study the intervention was administered to the whole network. In the second study two social networks are considered and in each only a subset of individuals, initially low/high in negative affect respectively received the intervention as `agents of change'. Data was analyzed using stochastic actor based modelling techniques to identify resulting network changes, impact on positive and negative affect and potential contagion of mood within the group. The first study found a group level increase in positive and a decrease in negative affect. Homophily was detected with regard to positive and negative affect but no evidence of contagion was found. The network itself became more volatile along with a fall in rate of change of negative affect. Centrality measures indicated that the best broadcasters were the individuals with the least negative affect levels at the beginning of the study. In the second study, the positive and negative affect levels for the whole group depended on the initial levels of negative affect of the intervention recipients. There was evidence of positive affect contagion in the group where intervention recipients had low initial level of negative affect and contagion in negative affect for the group where recipients had initially high level of negative affect.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Generic intertextuality in online social activism: the case of the It Gets Better project

The It Gets Better project has been held up as a model of successful social media activism. This article explores how narrators of It Gets Better videos make use of generic intertextuality, strategically combining the canonical narrative genres of the exemplum, the testimony, and the confession in a way that allows them to claim ‘textual authority’ and to make available multiple moral positions for themselves and their listeners. This strategy is further facilitated by the ambiguous participation frameworks associated with digital media, which make it possible for storytellers to tell different kinds of stories to different kinds of listeners at the same time, to simultaneously comfort the victims of anti-gay violence, confront its perpetrators, and elicit sympathy from ‘onlookers’. This analysis highlights the potential of new practices of online storytelling for social activism, and challenges notions that new media are contributing to the demise of common narrative traditions.

The role of social networks at different stages of business formation

This study empirically tests the fundamental assumption that social networks are important to entrepreneurs. This assumption underpins most social network research conducted in the field of entrepreneurship and is seldom questioned. Empirical data were drawn from Australia’s participation in the Global Entrepreneurship Monitor project (GEM) from 2000- 2005 – an aggregate sample of 14,205 randomly selected Australians. The study demonstrated: (1) statistically significant differences in social networks when entrepreneurs and non-entrepreneurs are compared and (2) that the structural diversity of social networks changes during the entrepreneurial process. It was found that structural diversity was most important to entrepreneurs in the discovery stage, least important to entrepreneurs in the start-up stage and of medium importance to entrepreneurs in the young business stage.