Network diffusion of gender diversity on boards: A process of two-speed opposing forces (original) (raw)

Active and passive diffusion processes in complex networks

Applied Network Science, 2018

Ideas, information, viruses: all of them, with their mechanisms, spread over the complex social information, viruses: all tissues described by our interpersonal relations. Usually, to simulate and understand the unfolding of such complex phenomena are used general mathematical models; these models act agnostically from the object of which they simulate the diffusion, thus considering spreading of virus, ideas and innovations alike. Indeed, such degree of abstraction makes it easier to define a standard set of tools that can be applied to heterogeneous contexts; however, it can also lead to biased, incorrect, simulation outcomes. In this work we introduce the concepts of active and passive diffusion to discriminate the degree in which individuals choice affect the overall spreading of content over a social graph. Moving from the analysis of a well-known passive diffusion schema, the Threshold model (that can be used to model peer-pressure related processes), we introduce two novel approaches whose aim is to provide active and mixed schemas applicable in the context of innovations/ideas diffusion simulation. Our analysis, performed both in synthetic and real-world data, underline that the adoption of exclusively passive/active models leads to conflicting results, thus highlighting the need of mixed approaches to capture the real complexity of the simulated system better.

Simple graph models of information spread in finite populations

Royal Society Open Science, 2015

We consider several classes of simple graphs as potential models for information diffusion in a structured population. These include biases cycles, dual circular flows, partial bipartite graphs and what we call 'single-link' graphs. In addition to fixation probabilities, we study structure parameters for these graphs, including eigenvalues of the Laplacian, conductances, communicability and expected hitting times. In several cases, values of these parameters are related, most strongly so for partial bipartite graphs. A measure of directional bias in cycles and circular flows arises from the non-zero eigenvalues of the antisymmetric part of the Laplacian and another measure is found for cycles as the value of the transition probability for which hitting times going in either direction of the cycle are equal. A generalization of circular flow graphs is used to illustrate the possibility of tuning edge weights to match pre-specified values for graph parameters; in particular, we show that generalizations of circular flows can be tuned to have fixation probabilities equal to the Moran probability for a complete graph by tuning vertex temperature profiles. Finally, single-link graphs are introduced as an example of a graph involving a bottleneck in the connection between two components and these are compared to the partial bipartite graphs. 2. Introduction Using graphs to represent structured populations has become an important tool in approaching a variety of questions relating to the way that information spreads in non-homogeneous populations. Questions that have been addressed include the extinction or fixation of mutant genes [1-4]; epidemics [5-7]; spread of computer viruses, rumours and gossip [8-11]; development of rumour spreading algorithms for synchronization processes in parallel computation [12-14]; uptake of innovations and new ideas [15]; locating the source of rumours or viruses (natural and computer) [16,17]; and tracking terrorists [18,19].

Social diffusion and global drift on networks

Physical Review E, 2015

We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is not state conservational and thus the global state of the network (i.e., sum of node states) will drift. The asymptotic average node state will be the average of initial node states weighted by their strengths. Here we show that, while the global state is not conserved in this process, the inner product of strength and state vectors is conserved instead, and perfect positive correlation between node states and local averages of their self/neighbor strength ratios always results in upward (or at least neutral) global drift. We also show that the strength assortativity negatively affects the speed of homogenization. Based on these findings, we propose an adaptive link weight adjustment method to achieve the highest upward global drift by increasing the strength-state correlation. The effectiveness of the method was confirmed through numerical simulations and implications for real-world social applications are discussed.

Impact of network structure on a model of diffusion and competitive interaction

EPL (Europhysics Letters), 2011

We consider a model in which agents of different species move over a complex network, are subject to reproduction and compete for resources. The complementary roles of competition and diffusion produce a variety of fixed points, whose stability depends on the structure of the underlying complex network. The survival and death of species is influenced by the network degree distribution, clustering, degree-degree correlations and community structures. We found that the invasion of all the nodes by just one species is possible only in Erdös-Renyi and regular graphs, while networks with scale-free degree distribution, as those observed in real social, biological and technological systems, guarantee the coexistence of different species and therefore help enhancing species diversity.

Diffusion and networks: A powerful combination!

Physica A: Statistical Mechanics and its Applications, 2005

Over the last decade, an enormous interest and activity in complex networks have been witnessed within the physics community. On the other hand, diffusion and its theory, have equipped the toolbox of the physicist for decades. In this paper, we will demonstrate how to combine these two seemingly different topics in a fruitful manner. In particular, we will review and develop further, an auxiliary diffusive process on weighted networks that represents a powerful concept and tool for studying network (community) structures. The working principle of the method is the observation that the relaxation of the diffusive process towards the stationary state is non-local and fastest in the highly connected regions of the network. This can be used to acquire non-trivial information about the structure of clustered and non-clustered networks.

Social Spreading in Complex Networks

2019

The scope of the research presented in this thesis is fairly broad, touching upon areas like social network analysis, information and behavioral contagion models, and social data science. As the world becomes increasingly digitalized, it becomes crucial to better understand interactions in the digital sphere. The proliferation of online communication allows interaction between people with more diverse backgrounds more varied areas of knowledge than before. However while increased digitalization carries the potential for an explosion of diversity in communication, that is far from the only conceivable consequence. The same diversity offers anyone online a multitude of different communities and sources of information. This carries the risk of individuals choosing disproportionately often to connect to individuals that are similar to themselves, and to consume exclusively information which supports their preexisting convictions. Fortunately fields such as network science, computational...

Equilibria in Social Networks with Heterogeneous Agents

Empirical literature shows that ex-ante asymmetries across players arise quite naturally in social network formation. In this work, a very general kind of heterogeneity is considered, and two different models of network formation are introduced corresponding to different kind of disutility of establishing direct connections. These models are games with vector valued payoffs which are here investigated by using the concept of Pareto-Nash equilibrium and its refinements. The processes of information diffusion within a group of individuals and their implication on how they affect social learning have attracted increasing interest in the economics literature. The analysis of these issues has developed in various directions; for instance, a first approach considers non-strategic agents while, in the literature on social networks, individuals are identified with the vertices of a graph and create strategically relationships (links) within the others in such a way that the level of connect...

Dynamics of social balance on networks

Physical Review E, 2005

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad-a triangular loop with one or three unfriendly links-is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"-all links are friendly-as the propensity p for friendly links in an update event passes through 1 / 2. A finite network always falls into a socially balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network not increase in an update is imposed, then the network quickly reaches a balanced final state. . Electronic address: redner@bu.edu FIG. 1. Imbalanced triads ⌬ 1 ͑left͒ and ⌬ 3 ͑right͒ and the possible outcomes after an update step by local triad dynamics. Solid and dashed lines represent friendly ͑e.g., s ij =1͒ and unfriendly ͑e.g., s ik =−1͒ relations, respectively.

The Impact of Structural Changes on Predictions of Diffusion in Networks

2008 IEEE International Conference on Data Mining Workshops, 2008

In a typical realistic scenario, there exist some past data about the structure of the network which are analyzed with respect to some possibly future spreading process, such as behavior, opinion, disease, or computer malware. How sensitive are the predictions made about spread and spreaders to the changes in the structure of the network? We investigate the answer to this question by considering seven realworld networks that have an explicit timeline and span a range of social interactions, from celebrity sightings to animal movement. For each dataset, we examine the results of the spread analysis with respect to the changes that occur in the network as the time unfolds as well as introduced random perturbations. We show that neither the estimates of the extent of spread for each individual nor the set of the top spreaders are robust to structural changes. Thus, analysis performed on historic data may not be relevant by the time it is acted upon.