This thesis studies two problems defined on complex networks, of which the first explores a conceivable extension of structural balance theory and the other concerns convergence issues in opinion dynamics. In the first half of the thesis we discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives (A, B, C) we reduce the (3!)3 = 216 possible configurations of triangles to 10 equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on n alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes. The second half of the thesis concerns an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a fully stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in rth moment. Avhandlingen studerar två problem definierade på komplexa nätverk, varav det första utforskar en tänkbar utökning av strukturell balansteori och det andra behandlar konvergensfrågor inom opinionsdynamik. I avhandlingens första hälft diskuteras möjliga definitioner på villkor för strukturell balans i ett nätverk med preferensordningar som nodattribut. Huvudresultatet är att för fallet med tre alternativ (A, B, C) så kan de (3!)3 = 216 möjliga konfigurationerna av trianglar reduceras till 10 ekvivalensklasser, vilka används som mått på en triangels balans som ett steg mot möjliga utökningar av strukturell balansteori. Vi härleder även en generell formel för antalet ekvivalensklasser för preferensordningar med n alternativ. Slutligen analyseras en empirisk datamängd och dess empiriska sannolikhetsfördelning av triangel-ekvivalensklasser jämförs med en nollhypotes i vilken preferenser tilldelas noderna slumpmässigt. Den andra hälften av avhandlingen rör en opinionsdynamikmodell där varje agent agerar slumpmässigt enligt en Bernoullifördelning vars sannolikhet uppdateras vid varje diskret tidssteg, och vi bevisar att denna modell konvergerar nästan säkert till konsensus. Vi ger också en detaljerad kritik av ett påstått bevis av detta resultat i litteraturen. Vi generaliserar resultatet genom att visa att antagandet om irreducibilitet i den ursprungliga modellen inte är nödvändigt. Vidare visar vi, som följdsats av det generaliserade resultatet, att den nästan säkra konvergensen till konsensus även håller om en agent är fullständigt envis och aldrig byter åsikt. I tillägg till detta visar vi att modellen, både i det ursprungliga och i det generaliserade fallet, konvergerar till konsensus även i r:te ordningens moment.

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeconomics and finance, and its purpose is to give readers an overview of several interesting topics for research at an intermediate level. Three different and interdisciplinary, but complementary, aspects of networks are put together in a single piece, namely: (i) complex networks theory, (ii) applied network analysis to social and economic interrelations, and (iii) dynamical evolution of systems and networks. The volume includes contributions from excellent scholars in economics and social sciences as well as leading experts in the fields of complex networks and nonlinear dynamics.

This self-contained text develops a Markov chain approach that makes the rigorous analysis of a class of microscopic models that specify the dynamics of complex systems at the individual level possible. It presents a general framework of aggregation in agent-based and related computational models, one which makes use of lumpability and information theory in order to link the micro and macro levels of observation. The starting point is a microscopic Markov chain description of the dynamical process in complete correspondence with the dynamical behavior of the agent-based model (ABM), which is obtained by considering the set of all possible agent configurations as the state space of a huge Markov chain. An explicit formal representation of a resulting “micro-chain” including microscopic transition rates is derived for a class of models by using the random mapping representation of a Markov process. The type of probability distribution used to implement the stochastic part of the model, which defines the updating rule and governs the dynamics at a Markovian level, plays a crucial part in the analysis of “voter-like” models used in population genetics, evolutionary game theory and social dynamics. The book demonstrates that the problem of aggregation in ABMs - and the lumpability conditions in particular - can be embedded into a more general framework that employs information theory in order to identify different levels and relevant scales in complex dynamical systems

A network is a mathematical object consisting of a set of points that are connected to each other in some fashion by lines. It turns out this simple description corresponds to a bewildering array of systems in the real world, ranging from technological ones such as the Internet and World Wide Web, biological networks such as that of connections of the nervous systems, food webs or protein interactions, infrastructural systems such as networks of roads, airports or the power-grid, to patterns of social and professional relationships such as friendship, sex partners, network of Hollywood actors, co-authorship networks and many more. Recent years have witnessed a substantial amount of interest within the scientific community in the properties of these networks. The emergence of the internet in particular, coupled with the widespread availability of inexpensive computing resources has facilitated studies ranging from large scale empirical analysis of networks in the real world, to the development of theoretical models and tools to explore the various properties of these systems. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology and the social sciences. This book brings together a collection of cutting-edge research in the field from a diverse array of researchers ranging from physicists to social scientists and presents them in a coherent fashion, highlighting the strong interconnections between the different areas. Topics included are social networks and social media, opinion and innovation diffusion, biological and health-related networks, language networks, as well as network theory, community detection, or growth models for Complex Networks.

This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the VI International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2017), which took place in Lyon on November 29 – December 1, 2017. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and ecological networks and technological networks.

Understanding the mechanism of a socio-economic system requires more than an understanding of the individuals that comprise the system. It also requires understanding how individuals interact with each other, and how the agg- gated outcome can be more than the sum of individual behaviors. This book contains the papers fostering the formation of an active multi-disciplinary community on socio-economic systems with the exciting new ?elds of age- based modeling and econophysics. We especially intend to increase the awareness of researchers in many ?elds with sharing the common view many economic and social activities as collectives of a large-scale heterogeneous and interacting agents. Economists seek to understand not only how individuals behave but also how the interaction of many individuals leads to complex outcomes. Age- based modeling is a method for studying socio-economic systems exhibiting the following two properties: (1) the system is composed of interacting agents, and (2) the system exhibits emergent properties, that is, properties arising from the interactions of the agents that cannot be deduced simply by agg- gating the properties of the system’s components. When the interaction of the agents is contingent on past experience, and especially when the agents continually adapt to that experience, mathematical analysis is typically very limited in its ability to derive the outcome.

This book highlights recent developments in the field of computer simulation and its application to social dynamics and behaviour. It covers latest advancements in the use of agent-based modelling by focusing on thematic issues, methodological progress and applications, including policy, industry and business. It aims to promote this interdisciplinary type of research by showing synergies, complementary and integration especially between computer sciences, social sciences, economics and organization, often bridging qualitative and quantitative research. The primary audience of this book are academics, practitioners and professionals using computer simulation for business counselling or industry.