Advances in Complex Systems

Community structure detection is widely accepted as a means of elucidating the functional properties of complex networks. The problem statement is ever evolving, with the aim of developing more flexible and realistic modeling procedures. For example, a first step in developing a more informative model is the inclusion of weighted interactions. In addition to the standard community structure problem, interest has increased in the detection of overlapping communities. Adopting such constraints may, in some cases, represent a more true to life abstraction of the system under study. In this paper, two novel mathematical programming algorithms for module detection are presented. First, disjoint modules in weighted and unweighted networks are detected by formulating modularity maximization as a mixed integer nonlinear programming (MINLP) model. The solution obtained is then used to detect overlapping modules through a further MINLP model. The inclusion of two parameters controlling the extent of overlapping offers flexibility in user requirements. Comparative results show that these methodologies perform competitively to previously proposed methods. The methodologies proposed here promote the detection of topological relationships in complex systems. Together with the amenable nature of mathematical programming models, we show that both algorithms offer a versatile solution to the community detection problem.

We consider a third party logistics service provider (LSP), who faces the problem of distributing different products from suppliers to consumers having no control on supply and demand. In a third party set-up, the operations of transport and storage are run as a black box for a fixed price. Thus the incentive for an LSP is to reduce its operational costs. The objective of this paper is to find an efficient network topology on a tactical level, which still satisfies the service level agreements on the operational level. We develop an optimization method, which constructs a tactical network topology based on the operational decisions resulting from a given model predictive control (MPC) policy. Experiments suggest that such a topology typically requires only a small fraction of all possible links. As expected, the found topology is sensitive to changes in supply and demand averages. Interestingly, the found topology appears to be robust to changes in second order moments of supply and demand distributions.

Evolution of cooperation has attracted considerable attention but so far no definitive answer exists. Probably each kind of problem has specific answers. This paper deals with evolution of cooperation in public goods games. We use random Boolean networks to formalize the non-local influence of K agents over a given agent. This formalism allows the representation of a variety of network regulation mechanisms by means of (i) different topologies and (ii) Boolean functions that do the regulation proper. However, random functions and connections do not necessarily lead to cooperation. Thus, it is necessary to find what kind of network structure is prone to promote cooperation. We employ an evolutionary approach to show that evolving the topologies and the random functions leads to much fitter structures.

We study Facebook networks at 40 American universities, with focus on the comparison of their degree distributions and mechanism governing their evolution. We find that the heterogeneity indexes of these networks are all small compared with scale-free networks, and different from real-world social networks 5 Facebook networks show significant degree disassortativity; the exponent γ for the power-law model of the degree distributions is large for the networks, indicating obvious homogeneity of network structure. We calculate the goodness-of-fit between the data and power law and find that the p-values are larger than threshold 0.1 for 20 networks, implying that power law is a plausible hypothesis; we compare the power-law model with 4 alternative competing distributions and find that power-law model gives the best fit for all 40 networks. However in wider interval of degrees some other distributions, such as log-normal or stretched exponential, can give the best fit. Further based on the homogeneity of Facebook we propose an analyzable model that integrates the introduction of new vertices and edges. The edges can be established either between new vertices and old vertices or between old vertices. The model captures the real evolution processes of Facebook networks and can well reproduce their degree distributions.

Using the fact that connections between vertices of a network often represent directed and weighted flows, we apply hydraulic principles to develop novel insights into network structure and growth. We develop a network model based on Bernoulli's principle and use it to analyze changes in network properties. Simulation results show that velocity of flow, resistance, fitness and existing connections in a system determine network connections of a vertex as well as overall network structure. We demonstrate how network structure is affected by changes in velocity and resistance, and how one vertex can monopolize connections within a network. Using Bernoulli's principle, we are able to independently reproduce key results in the network literature.

The correlation matrix of stocks returns is used in order to create maps of the São Paulo Stock Exchange (BM&F-Bovespa), Brazil's main stock exchange. The data refer to the year 2010, and the correlations between stock returns lead to the construction of a minimum spanning tree and of asset graphs with a variety of threshold values. The results are analyzed using techniques of network theory. Also, using data from 2007 to 2010, a study is made on the dynamics of the network formed by stocks from that same stock exchange.