Viability in dynamic social networks

Two examples, Sampson's monks and Padgett and Ansell’ Florentines, illustrate the viability approach of dynamic networks. Notably, the relationship with centrality is studied. Historical processes involving networks are discussed.

Networks are presented as controls in controlled dynamic systems. Viability is the property for a state x that there exists a trajectory starting from x and satisfying the constraints until the time horizon. To obtain this, connection matrices must be selected at each time and each visited state among a specific set, the regulation map, which is carefully defined and built.     

The effect of gossip on social networks

In this article, we develop a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A‐B and weakens both B‐C and A‐C. We find, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations show that the effect of gossip on network metrics (clustering coefficient, average‐path‐length, and sum‐of‐strengths) varies with network structure and average‐node‐degree. © 2010 Wiley Periodicals, Inc. Complexity 16: 39‐47, 2011     

Interacting neural networks and the emergence of social structure

The article describes a computational model for the simulation of the emergence of social structure or social order, respectively. The model is theoretically based on the theory of social typifying by Berger and Luckmann. It consists of interacting artificial actors (agents), which are represented by two neural networks, an action net, and a perception net. By mutually adjusting of their actions, the agents are able to constitute a self‐organized social order in dependency of their personal characteristics and certain features of their environment. A fictitious example demonstrates the applicability of the model to problems of extra‐terrestrial robotics. © 2007 Wiley Periodicals, Inc. Complexity 12: 41–52, 2007     

The cohesiveness of subgroups in social networks: A view from game theory

A family of cohesiveness measures, based on game theoretical concepts, is proposed for subgroups in social networks. Given a communication situation, consisting of a coalitional game and a graph, both defined on the same set of players-nodes, cohesiveness of a subset is defined as the proportion of their worth that the players in subset retain, when the originally deterministic (restricted) graph becomes a probabilistic one (in a specific manner). Conditions on the game are given to reach some desirable properties.     

Activation clustering in neural and social networks

Questions related to the evolution of the structure of networks have received recently a lot of attention in the literature. But what is the state of the network given its structure? For example, there is the question of how the structures of neural networks make them behave? Or, in the case of a network of humans, the question could be related to the states of humans in general, given the structure of the social network. The models based on stochastic processes developed in this article, do not attempt to capture the fine details of social or neural dynamics. Rather they aim to describe the general relationship between the variables describing the network and the aggregate behavior of the network. A number of nontrivial results are obtained using computer simulations. © 2005 Wiley Periodicals, Inc. Complexity 10: 42–50, 2005     

An algebraic theory of strong power in negatively connected exchange networks

Various extensions of the model are proposed to deal with a wider variety of conditions than are normally examined in experiments on exchange networks. With little or no modification, the model can predict power when exchange relations are unequal in value, when positions vary in the number of exchanges in which they can participate, and when three or more participants are required for a transaction to occur.

A structural and algebraic theory of power in negatively connected exchange networks can be deduced from a few simple and plausible assumptions about how individuals make decisions. The model generates a set of equations. A typology of exchange networks follows from characteristics of the solution to these equations. There are four possibilities: the equations have a unique solution in which some positions have all the power; the equations have a unique solution in which all positions have equal power; the equations have an infinity of solutions, in which case power is undetermined by structural considerations; the equations have no solution, in which case power should be unstable.     

Unanimous opinions in social influence networks

In this paper, I show that persons reach unanimous opinions even when they have different initial opinions and different social influences in social influence networks. Friedkin and Johnsen introduced a model of social influence networks, and identified conditions for initially diverse opinions to converge. However, they did not examine conditions of “unanimous” convergence. Hence, I provide sufficient conditions of such unanimous consensus by focusing on three typical but conflicting social influences: the equal influence, the influence of the lowest opinion, and no influence. I show that unanimous opinions occur even when persons have antagonistic social influences such as the equal influence and the influence of the lowest opinion. I also demonstrate that the most cooperative type is the equal influence, but the most central type is the no influence.     

Sensitivity of chemical reaction networks: A structural approach. 3. Regular multimolecular systems

We present a systematic mathematical analysis of the qualitative steady‐state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions, multiple reaction products, nonmonotone rate functions, and non‐closed autonomous systems. Our structural sensitivity analysis is based on the stoichiometry of the reaction network, only. It does not require numerical data on reaction rates. Instead, we impose mild and generic nondegeneracy conditions of algebraic type. From the structural data, only, we derive which steady‐state concentrations are sensitive to, and hence influenced by, changes of any particular reaction rate—and which are not. We also establish transitivity properties for influences involving rate perturbations. This allows us to derive an influence graph which globally summarizes the influence pattern of any given network. The influence graph allows the computational, but meaningful, automatic identification of functional subunits in general networks, which hierarchically influence each other. We illustrate our results for several variants of the glycolytic citric acid cycle. Biological applications include enzyme knockout experiments and metabolic control.     

On effectiveness of wiretap programs in mapping social networks

Snowball sampling methods are known to be a biased toward highly connected actors and consequently produce core-periphery networks when these may not necessarily be present. This leads to a biased perception of the underlying network which can have negative policy consequences, as in the identification of terrorist networks. When snowball sampling is used, the potential overload of the information collection system is a distinct problem due to the exponential growth of the number of suspects to be monitored. In this paper, we focus on evaluating the effectiveness of a wiretapping program in terms of its ability to map the rapidly evolving networks within a covert organization. By running a series of simulation-based experiments, we are able to evaluate a broad spectrum of information gathering regimes based on a consistent set of criteria. We conclude by proposing a set of information gathering programs that achieve higher effectiveness then snowball sampling, and at a lower cost. Maksim Tsvetovat is an Assistant Professor at the Center for Social Complexity and department of Public and International Affairs at George Mason University, Fairfax, VA. He received his Ph.D. from the Computation, Organizations and Society program in the School of Computer Science, Carnegie Mellon University. His dissertation was centered on use of artificial intelligence techniques such as planning and semantic reasoning as a means of studying behavior and evolution of complex social networks, such as these of terrorist organizations. He received a Master of Science degree from University of Minnesota with a specialization in Artificial Intelligence and design of Multi-Agent Systems, and has also extensively studied organization theory and social science research methods. His research is centered on building high-fidelity simulations of social and organizational systems using concepts from distributed artificial intelligence and multi-agent systems. Other projects focus on social network analysis for mapping of internal corporate networks or study of covert and terrorist orgnaizations. Maksim’s vita and publications can be found on Kathleen M. Carley is a professor in the School of Computer Science at Carnegie Mellon University and the director of the center for Compuational Analysis of Social and Organizational Systems (CASOS) which has over 25 members, both students and research staff. Her research combines cognitive science, social networks and computer science to address complex social and organizational problems. Her specific research areas are dynamic network analysis, computational social and organization theory, adaptation and evolution, text mining, and the impact of telecommunication technologies and policy on communication, information diffusion, disease contagion and response within and among groups particularly in disaster or crisis situations. She and her lab have developed infrastructure tools for analyzing large scale dynamic networks and various multi-agent simulation systems. The infrastructure tools include ORA, a statistical toolkit for analyzing and visualizing multi-dimensional networks. ORA results are organized into reports that meet various needs such as the management report, the mental model report, and the intelligence report. Another tool is AutoMap, a text-mining systems for extracting semantic networks from texts and then cross-classifying them using an organizational ontology into the underlying social, knowledge, resource and task networks. Her simulation models meld multi-agent technology with network dynamics and empirical data. Three of the large-scale multi-agent network models she and the CASOS group have developed in the counter-terrorism area are: BioWar a city-scale dynamic-network agent-based model for understanding the spread of disease and illness due to natural epidemics, chemical spills, and weaponized biological attacks; DyNet a model of the change in covert networks, naturally and in response to attacks, under varying levels of information uncertainty; and RTE a model for examining state failure and the escalation of conflict at the city, state, nation, and international as changes occur within and among red, blue, and green forces. She is the founding co-editor with Al. Wallace of the journal Computational Organization Theory and has co-edited several books and written over 100 articles in the computational organizations and dynamic network area. Her publications can be found at: http://www.casos.cs.cmu.edu/bios/carley/publications.php     

A graph-theoretic approach to exponential stability of BAM neural networks with delays and reaction-diffusion

This paper deals with the problem of global exponential stability for bidirectional associate memory (BAM) neural networks with time-varying delays and reaction-diffusion terms. By using some inequality techniques, graph theory as well as Lyapunov stability theory, a systematic method of constructing a global Lyapunov function for BAM neural networks with time-varying delays and reaction-diffusion terms is provided. Furthermore, two different kinds of sufficient principles are derived to guarantee the exponential stability of BAM neural networks. Finally, a numerical example is carried out to demonstrate the effectiveness and applicability of the theoretical results.     

Position-specific information in social networks: Are you connected?

Individuals in social networks often imperfectly monitor others’ network relationships and have incomplete information about the value of forming new relationships. This paper introduces the Generalized Conjectural Equilibrium (GCE) concept for such settings and completely characterizes the set of GCE networks when players observe only local parts of the network. Incomplete information and imperfect monitoring generate different types of inefficiency. These inefficiencies increase in number and scope as network observation becomes more localized. These results suggest that actual social networks will be structured inefficiently in general.     

A case study of cracks in the scientific enterprise: Reinvention of information‐theoretic measures for graphs

This article calls attention to flaws in the scientific enterprise, providing a case study of the lack of professionalism in published journal articles in a particular area of research, namely, network complexity. By offering details of a special case of poor scholarship, which is very likely indicative of a broader problem, the authors hope to stimulate editors and referees to greater vigilance, and to strengthen authors' resolve to take their professional responsibilities more seriously. © 2014 Wiley Periodicals, Inc. Complexity 21: 10–14, 2016     

An algorithm for detecting community structure of social networks based on prior knowledge and modularity

An algorithm is proposed to detect community structure in social network. The algorithm begins with a community division based on prior knowledge of the degrees of the nodes, and then combines the communities until a clear partition is obtained. In applications such as a computer‐generated network, Ucinet networks, and Chinese rural‐urban migrants' social networks, the algorithm can achieve higher modularity and greater speed than others in the recent literature. © 2007 Wiley Periodicals, Inc. Complexity 12: 53–60, 2007     

An exploration of social identity: The structure of the BBC news‐sharing community on Twitter

Online social media influence the flow of news and other information, potentially altering collective social action while generating a large volume of data useful to researchers. Mapping these networks may make it possible to predict the course of social and political movements, technology adoption, and economic behavior. Here, we map the network formed by Twitter users sharing British Broadcasting Corporation (BBC) articles. The global audience of the BBC is primarily organized by language with the largest linguistic groups receiving news in English, Spanish, Russian, and Arabic. Members of the network primarily “follow” members sharing articles in the same language, and these audiences are primarily located in geographical regions where the languages are native. The one exception to this rule is a cluster interested in Middle East news which includes both Arabic and English speakers. We further analyze English‐speaking users, which differentiate themselves into four clusters: one interested in sports, two interested in United Kingdom (UK) news—with word usage suggesting this reflects political polarization into Conservative and Labour party leanings—and a fourth group that is the English speaking part of the group interested in Middle East news. Unlike the previously studied New York Times news sharing network the largest scale structure of the BBC network does not include a densely connected group of globally interested and globally distributed users. The political polarization is similar to what was found for liberal and conservative groups in the New York Times study. The observation of a primary organization of the BBC audience around languages is consistent with the BBC's unique role in history as an alternative source of local news in regions outside the UK where high quality uncensored news was not available. © 2014 Wiley Periodicals, Inc. Complexity 19: 55–63, 2014     

Quantifying the complexity of flow networks: How many roles are there?

Weighted flow networks are structures that arise naturally when analyzing complex systems. The countable properties of unweighted networks are not easily generalized to weighted networks. One candidate measure of complexity is the number of roles, or specialized functions in a network. It is easy to identify the number of roles in a linear or cyclic unweighted network. There is only one logically consistent way to generalize the measures of nodes, flows, connectivity, and roles into weighted networks, and these generalizations are equivalent to indices derived from information theory and used by ecologists since the late seventies. Data from ecosystem networks suggests that ecosystems inhabit a narrow window of the parameter space defined by these measures. © 2003 Wiley Periodicals, Inc.     

Common cold outbreaks: A network theory approach

In this study, at first we evaluated the network structure in social encounters by which respiratory diseases can spread. We considered common-cold and recorded a sample of human population and actual encounters between them. Our results show that the database structure presents a great value of clustering. In the second step, we evaluated dynamics of disease spread with SIR model by assigning a function to each node of the structural network. The rate of disease spread in networks was observed to be inversely correlated with characteristic path length. Therefore, the shortcuts have a significant role in increasing spread rate. We conclude that the dynamics of social encounters’ network stands between the random and the lattice in network spectrum. Although in this study we considered the period of common-cold disease for network dynamics, it seems that similar approaches may be useful for other airborne diseases such as SARS.