Evolutionary prisoner's dilemma game on Barabási–Albert scale-free networks

An evolutionary prisoner's dilemma game (PDG) with players located on Barabási–Albert scale-free networks (BASFN) with average connectivity 8$8$ is studied in detail. The players are pure strategists and can adopt two strategies: either defect or cooperate. Several alternative update rules determining the evolution of each player's strategy are considered. Using Monte Carlo (MC) simulations we implemented both synchronous and asynchronous update dynamics to calculate the average density of cooperators _ρC${\rho }_C$ as a function of the temptation-to-defect b$b$ in the equilibrium state. For the sake of comparison, evolution of cooperative behavior on random regular graphs (RRG) and regular lattices (RL) with the same total size and average connectivity as BASFN are also investigated. We find the overall result that cooperation is sometimes inhibited and sometimes enhanced on the BASFN, with respect to the cases on the RRG and RL. The differences depend on the detailed evaluation function of the players’ success (average payoffs of the players in the present case), the different update rules that determine a player's future strategy, the synchronous and asynchronous events of strategy-updating, and also on the temptation to defect.     

An evolutionary model of social networks

Social networks in communities, markets, and societies self-organise through the interactions of many individuals. In this paper we use a well-known mechanism of social interactions — the balance of sentiment in triadic relations — to describe the development of social networks. Our model contrasts with many existing network models, in that people not only establish but also break up relations whilst the network evolves. The procedure generates several interesting network features such as a variety of degree distributions and degree correlations. The resulting network converges under certain conditions to a steady critical state where temporal disruptions in triangles follow a power-law distribution.     

The dynamics of a mobile phone network

The empirical study of network dynamics has been limited by the lack of longitudinal data. Here we introduce a quantitative indicator of link persistence to explore the correlations between the structure of a mobile phone network and the persistence of its links. We show that persistent links tend to be reciprocal and are more common for people with low degree and high clustering. We study the redundancy of the associations between persistence, degree, clustering and reciprocity and show that reciprocity is the strongest predictor of tie persistence. The method presented can be easily adapted to characterize the dynamics of other networks and can be used to identify the links that are most likely to survive in the future.     

The spreading of opposite opinions on online social networks with authoritative nodes

The study of opinion dynamics, such as spreading and controlling of rumors, has become an important issue on social networks. Numerous models have been devised to describe this process, including epidemic models and spin models, which mainly focus on how opinions spread and interact with each other, respectively. In this paper, we propose a model that combines the spreading stage and the interaction stage for opinions to illustrate the process of dispelling a rumor. Moreover, we set up authoritative nodes, which disseminate positive opinion to counterbalance the negative opinion prevailing on online social networking sites. With analysis of the relationship among positive opinion proportion, opinion strength and the density of authoritative nodes in networks with different topologies, we demonstrate that the positive opinion proportion grows with the density of authoritative nodes until the positive opinion prevails in the entire network. In particular, the relationship is linear in homogeneous topologies. Besides, it is also noteworthy that initial locations of the negative opinion source and authoritative nodes do not influence positive opinion proportion in homogeneous networks but have a significant impact on heterogeneous networks. The results are verified by numerical simulations and are helpful to understand the mechanism of two different opinions interacting with each other on online social networking sites.     

Obtaining communities with a fitness growth process

The study of community structure became an important topic of research over the last years. But, while successfully applied in several areas, the concept lacks of a general and precise notion. Facts like the hierarchical structure and heterogeneity of complex networks make it difficult to unify the idea of community and its evaluation. The global functional known as modularity is probably the most used technique in this area. Nevertheless, its limits have been deeply studied. Local techniques as the one by Lancichinetti et al. (2009) [1] arose as an answer to the resolution limit and degeneracies that modularity has.     

A social communication model based on simplicial complexes

Networks offer a powerful language with which to describe and study pairwise interaction. However, in many contexts, these rich collective phenomena require a higher-order approach to encode dynamical processes — for example in idea integration and information transmission (co-publication is a particularly familiar example). Here we introduce a novel framework for social communication by reshaping the networked system to be a simplicial complex, where the communication involves the interaction not only of individual nodes but also among cliques to which they belong. Simplicial complexes extend the network-based pairwise relationship to multiagent interaction. Assuming that the same individual in different cliques may play different roles, a threshold is designed and combined with the node state to determine the clique state. We employ the discrete microscopic Markov chain approach to model the simplex-based social communication and then obtain the underlying critical condition for information outbreaks. Moreover, we perform extensive numerical analysis of the proposed simplicial complex-based communication model and compare its performance with Monte Carlo simulation.     

Where do we stand on econophysics?

This issue contains papers selected from the contributions presented at the 5th International Conference on “Applications of Physics in Financial Analysis” (APFA5) held in Torino from June 29th to July 1st, 2006 (http://www.polito.it/apfa5). The issue collects recent applications of models and methods of statistical physics to economic problems. This interdisciplinary field of research, known as Econophysics, has seen intensive growth over the last decade. The challenge for econophysicists will be to go beyond the traditional views of economics and physics unifying the separate lines of development followed by the two disciplines over great part of the 20th century.“The conventional view serves to protect us from the painful job of thinking”, John Kenneth Galbraith (1908-2006).     

Effective mechanism for social recommendation of news

Recommender systems represent an important tool for news distribution on the Internet. In this work we modify a recently proposed social recommendation model in order to deal with no explicit ratings of users on news. The model consists of a network of users which continually adapts in order to achieve an efficient news traffic. To optimize the network’s topology we propose different stochastic algorithms that are scalable with respect to the network’s size. Agent-based simulations reveal the features and the performance of these algorithms. To overcome the resultant drawbacks of each method we introduce two improved algorithms and show that they can optimize the network’s topology almost as fast and effectively as other not-scalable methods that make use of much more information.     

Relaxation in systems with hierarchical organization: Analytical derivation of the relaxation and dispersion functions

We report a successful attempt to derive a closed-form expression for the relaxation function of a complex system by solving a set of coupled kinetic equations connecting the excitation/de-excitation rates to the number of particles (such as electrical charges, dipoles, etc.) in excited states. Our approach, originating from developments in dielectric and mechanical relaxation studies, allows the use of a unified treatment for a wide array of natural processes which often pose challenges to theoretical modeling. We use the notions that (i) a dipole represents any pair formed by a particle in an excited state (such as an energy level in optically excited molecules, or an electrode in dielectric spectroscopy) and its image in the ground state (or reference electrode), that (ii) coupling between such dipoles may be described as particle transfer from one excited state to another with lower energy, and that (iii) the relaxation function for such a system of dipoles is mathematically equivalent to the cumulative distribution function of particles, i.e., the total number of particles that are still in an excited state at a time t following excitation. Taken together, these ideas naturally lead to the identification of two types of relaxation – parallel and serial relaxation – and allow one to tackle systems with either geometrical or physical self-similarity within a unified mathematical scheme.     

Users structure and behavior on an online social network during a political protest

Over the past years, new technologies and specially online social networks have penetrated into the world’s population at an accelerated pace. In this paper we analyze collected data from the web application Twitter, in order to describe the structure and dynamics of the emergent social networks, based on complexity science. We focused on a Venezuelan protest that took place exclusively by Twitter during December, 2010. We found a community structure with highly connected hubs and three different kinds of user behavior that determine the information flow dynamics. We noticed that even though online social networks appear to be a pure social environment, traditional media still holds loads of influence inside the network.     

Phase transitions in social networks

We study a model of network with clustering and desired node degree. The original purpose of the model was to describe optimal structures of scientific collaboration in the European Union. The model belongs to the family of exponential random graphs. We show by numerical simulations and analytical considerations how a very simple Hamiltonian can lead to surprisingly complicated and eventful phase diagram.     

Self organization of social hierarchy and clusters in a challenging society with free random walks

Emergence of social hierarchy and clusters in a challenging equal-right society is studied on the basis of the agent-based model, where warlike individuals who have own power or wealth perform random walks in a random order on a lattice and when meeting others the individuals challenge the strongest among the neighbors. We assume that the winning probability depends on the difference in their wealth and after the fight the winner gets and the loser loses a unit of the wealth. We show that hierarchy is self organized when the population exceeds a critical value and the transition from egalitarian state to hierarchical state occurs in two steps. The first transition is continuous to the society with widespread winning-probability. At the second transition the variance of the winning fraction decrease discontinuously, which was not observed in previous studies. The second hierarchical society consists of a small number of extreme winners and many individuals in the middle class and losers. We also show that when the relaxation parameter for the wealth is large, the first transition disappears. In the second hierarchical society, a giant cluster of individuals is formed with a layered structure in the power order and some people stray around it. The structure of the cluster and the distribution of wealth are quite different from the results of the previous challenging model [M. Tsujiguchi and T. Odagaki, Physica A 375 (2007) 317] which adopts the preassigned order for random walk.     

Limited resolution in complex network community detection with Potts model approach

According to Fortunato and Barthélemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.     

Hierarchy,cities size distribution and Zipf's law

We show that a hierarchical cities structure can be generated by a self-organized process which grows with a bottom-up mechanism, and that the resulting distribution is power law. First we analytically prove that the power law distribution satisfies the balance between the offer of the city and the demand of its basin of attraction, and that the exponent in the Zipf's law corresponds to the multiplier linking the population of the central city to the population of its basin of attraction. Moreover, the corresponding hierarchical structure shows a variable spanning factor, and the population of the cities linked to the same city up in the hierarchy is variable as well. Second a stochastic dynamic spatial model is proposed, whose numerical results confirm the analytical findings. In this model, inhabitants minimize the transportation cost, so that the greater the importance of this cost, the more stable is the system in its microscopic aspect. After a comparison with the existent methods for the generation of a power law distribution, conclusions are drawn on the connection of hierarchical structure, and power law distribution, with the functioning of the system of cities.     

Order-disorder phase transition in a cliquey social network

We investigate the network model of community by Watts, Dodds and Newman (D.J. Watts et al., Science 296, 1302 (2002)) as a hierarchy of groups, each of 5 individuals. A homophily parameter α controls the probability proportional to exp (-αx) of selection of neighbours against distance x. The network nodes are endowed with spin-like variables s_i = ± 1, with Ising interaction J > 0. The Glauber dynamics is used to investigate the order-disorder transition. The transition temperature T_c is close to 3.8 for α < 0.0 and it falls down to zero above this value. The result provides a mathematical illustration of the social ability to a collective action via weak ties, as discussed by Granovetter in 1973.     

The backbone of a city

Recent studies have revealed the importance of centrality measures to analyze various spatial factors affecting human life in cities. Here we show how it is possible to extract the backbone of a city by deriving spanning trees based on edge betweenness and edge information. By using as sample cases the cities of Bologna and San Francisco, we show how the obtained trees are radically different from those based on edge lengths, and allow an extended comprehension of the “skeleton” of most important routes that so much affects pedestrian/vehicular flows, retail commerce vitality, land-use separation, urban crime and collective dynamical behaviours.     

Fluctuation theorems in inhomogeneous media under coarse graining

We compare the fluctuation relations for work and entropy in underdamped and overdamped systems, when the friction coefficient of the medium is space-dependent. We find that these relations remain unaffected in both cases. We have restricted ourselves to Stratonovich discretization scheme for the overdamped case.     

Analysis and models of bilateral investment treaties using a social networks approach

Bilateral investment treaties (BITs) are agreements between two countries for the reciprocal encouragement, promotion and protection of investments in each other’s territories by companies based in either country. Germany and Pakistan signed the first BIT in 1959 and since then, BITs are one of the most popular and widespread form of international agreement. In this work we study the proliferation of BITs using a social networks approach. We propose a network growth model that dynamically replicates the empirical topological characteristics of the BIT network.     

Human behavior in online social systems

We present and study data concerning human behavior in four online social systems: (i) an Internet community of friends of over 10⁷ people, (ii) a music community website with over 10⁶ users, (iii) a gamers’ community server with over 5 × 10⁶ users and (iv) a booklovers’ website with over 2.5 × 10⁵ users. The purpose of those systems is different; however, their properties are very similar. We have found that the distribution of human activity (e.g., the sum of books read or songs played) has the form of a power law. Moreover, the relationship between human activity and time has a power-law form, too. We present a simple interest-driven model of the evolution of such systems which explains the emergence of two scaling regimes.