The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore the tools of statistical physics and nonlinear dynamics has been proved to be very useful the underlying dynamics of the system. In this paper we introduce the concept of the multidisciplinary field of econophysics, a neologism that denotes the activities of Physicists who are working on economic problems to test a variety of new conceptual approaches deriving from the physical science and review the recent developments in the discipline and possible future trends.

The conventional wisdom is that social networks exhibit an assortative mixing pattern, whereas biological and technological networks show a disassortative mixing pattern. However, the recent research on the online social networks modifies the widespread belief, and many online social networks show a disassortative or neutral mixing feature. Especially, we found that an online social network, Wealink, underwent a transition from degree assortativity characteristic of real social networks to degree disassortativity characteristic of many online social networks, and the transition can be reasonably elucidated by a simple network model that we propose. The relations among network assortativity, clustering, and modularity are also discussed in the paper.

As individuals communicate, their exchanges form a dynamic network. We demonstrate, using time series analysis of communication in three online settings, that network structure alone can be highly revealing of the diversity and novelty of the information being communicated. Our approach uses both standard and novel network metrics to characterize how unexpected a network configuration is, and to capture a network's ability to conduct information. We find that networks with a higher conductance in link structure exhibit higher information entropy, while unexpected network configurations can be tied to information novelty. We use a simulation model to explain the observed correspondence between the evolution of a network's structure and the information it carries.

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The local properties of the network are affected by the surface genus which, for example, produces significant changes in the degree distribution and in the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwoveness, changing the scaling properties from large-world-kind (small genus) to small- and ultra-small-world-kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description. Within such a framework, we study the properties of topologically-embedded graphs at high and low `temperatures' observing the formation of increasingly regular structures by cooling the system. We show that the cooling dynamics is strongly affected by the surface genus with the manifestation of a glassy-like freezing transitions occurring when the amount of topological disorder is low.

For several decades, a leading paradigm of how to quantitatively assess scientific research has been the analysis of the aggregated citation information in a set of scientific publications. Although the representation of this information as a citation network has already been coined in the 1960s, it needed the systematic indexing of scientific literature to allow for impact metrics that actually made use of this network as a whole improving on the then prevailing metrics that were almost exclusively based on the number of direct citations. However, besides focusing on the assignment of credit, the paper citation network can also be studied in terms of the proliferation of scientific ideas. Here we introduce a simple measure based on the shortest-paths in the paper's in-component or, simply speaking, on the shape and size of the wake of a paper within the citation network. Applied to a citation network containing Physical Review publications from more than a century, our approach is able to detect seminal articles which have introduced concepts of obvious importance to the further development of physics. We observe a large fraction of papers co-authored by Nobel Prize laureates in physics among the top-ranked publications.

A novel algorithm for actively trading stocks is presented. While traditional expert advice and "universal" algorithms (as well as standard technical trading heuristics) attempt to predict winners or trends, our approach relies on predictable statistical relations between all pairs of stocks in the market. Our empirical results on historical markets provide strong evidence that this type of technical trading can "beat the market" and moreover, can beat the best stock in the market. In doing so we utilize a new idea for smoothing critical parameters in the context of expert learning.

A discrete-time version of the replicator equation for two-strategy games is studied. The stationary properties differ from that of continuous time for sufficiently large values of the parameters, where periodic and chaotic behavior replace the usual fixed-point population solutions. We observe the familiar period-doubling and chaotic-band-splitting attractor cascades of unimodal maps but in some cases more elaborate variations appear due to bimodality. Also unphysical stationary solutions have unusual physical implications, such as uncertainty of final population caused by sensitivity to initial conditions and fractality of attractor preimage manifolds.

How to distribute welfare in a society is a key issue in the subject of distributional justice, which is deeply involved with notions of fairness. Following a thought experiment by Dworkin, this work considers a society of individuals with different preferences on the welfare distribution and an official to mediate the coordination among them. Based on a simple assumption that an individual's welfare is proportional to how her preference is fulfilled by the actual distribution, we show that an egalitarian preference is a strict Nash equilibrium and can be favorable even in certain inhomogeneous situations. These suggest how communication can encourage and secure a notion of fairness.

We consider the performance of non-optimal hedging strategies in exponential L\'evy models. Given that both the payoff of the contingent claim and the hedging strategy admit suitable integral representations, we use the Laplace transform approach of Hubalek et al. (2006) to derive semi-explicit formulas for the resulting mean squared hedging error in terms of the cumulant generating function of the underlying L\'evy process. In two numerical examples, we apply these results to compare the efficiency of the Black-Scholes hedge and the model delta to the mean-variance optimal hedge in a normal inverse Gaussian and a diffusion-extended CGMY L\'evy model.

Models of message flows in an artificial group of users communicating via the Internet are introduced and investigated using numerical simulations. We assumed that messages possess an emotional character with a positive valence and that the willingness to send the next affective message to a given person increases with the number of messages received from this person. As a result, the weights of links between group members evolve over time. Memory effects are introduced, taking into account that the preferential selection of message receivers depends on the communication intensity during the recent period only. We also model the phenomenon of secondary social sharing when the reception of an emotional e-mail triggers the distribution of several emotional e-mails to other people.