Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of complex networks therefore rely on the use of measurements capable of expressing the most relevant topological features. This article presents a survey of such measurements. It includes general considerations about complex network characterization, a brief review of the principal models, and the presentation of the main existing measurements. Important related issues covered in this work comprise the representation of the evolution of complex networks in terms of trajectories in several measurement spaces, the analysis of the correlations between some of the most traditional measurements, perturbation analysis, as well as the use of multivariate statistics for feature selection and network classification. Depending on the network and the analysis task one has in mind, a specific set of features may be chosen. It is hoped that the present survey will help the proper application and interpretation of measurements.

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Pattern recognition has been employed in a myriad of industrial, commercial and academic applications. Many techniques have been devised to tackle such a diversity of applications. Despite the long tradition of pattern recognition research, there is no technique that yields the best classification in all scenarios. Therefore, as many techniques as possible should be considered in high accuracy applications. Typical related works either focus on the performance of a given algorithm or compare various classification methods. In many occasions, however, researchers who are not experts in the field of machine learning have to deal with practical classification tasks without an in-depth knowledge about the underlying parameters. Actually, the adequate choice of classifiers and parameters in such practical circumstances constitutes a long-standing problem and is one of the subjects of the current paper. We carried out a performance study of nine well-known classifiers implemented in the Weka framework and compared the influence of the parameter configurations on the accuracy. The default configuration of parameters in Weka was found to provide near optimal performance for most cases, not including methods such as the support vector machine (SVM). In addition, the k-nearest neighbor method frequently allowed the best accuracy. In certain conditions, it was possible to improve the quality of SVM by more than 20% with respect to their default parameter configuration.

Most real complex networks--such as protein interactions, social contacts, and the Internet--are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key issue to investigate and characterize how effectively the nodes and edges of such networks can be covered by different strategies. At the same time, it is critically important to infer how well can topological measurements such as the average node degree and average clustering coefficient be estimated during such network explorations. The present article addresses these problems by considering random, Barabási-Albert (BA), and geographical network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes. A series of relevant results are obtained, including the fact that networks of the three studied models with the same size and average node degree allow similar node and edge coverage efficiency, the identification of linear scaling with the size of the network of the random walk step at which a given percentage of the nodes/edges is covered, and the critical result that the estimation of the averaged node degree and clustering coefficient by random walks on BA networks often leads to heavily biased results. Many are the theoretical and practical implications of such results.

Election results are determined by numerous social factors that affect the formation of opinion of the voters, including the network of interactions between them and the dynamics of opinion influence. In this work we study the result of proportional elections using an opinion dynamics model similar to simple opinion spreading over a complex network. Erdös-Rényi, Barabási-Albert, regular lattices, and randomly augmented lattices are considered as models of the underlying social networks. The model reproduces the power law behavior of a number of candidates with a given number of votes found in real elections with the correct slope, a cutoff for a larger number of votes, and a plateau for a small number of votes. It is found that the small world property of the underlying network is fundamental for the emergence of the power law regime.

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small-world properties of real networks were fundamental to stimulate more realistic models and to understand important dynamical processes related to network growth. However, the properties of the network borders (nodes with degree equal to 1), one of its most fragile parts, remained little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze the border trees of complex networks, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider how their topological properties can be quantified in terms of their depth and number of leaves. We investigate the properties of border trees for several theoretical models as well as real-world networks. Among the obtained results, we found that more than half of the nodes of some real-world networks belong to the border trees. A power-law with cut-off was observed for the distribution of the depth and number of leaves of the border trees. An analysis of the local role of the nodes in the border trees was also performed.

We consider the implementation of a parallel Monte Carlo code for high-performance simulations on PC clusters with MPI. We carry out tests of speedup and efficiency. The code is used for numerical simulations of pure SU (2) lattice gauge theory at very large lattice volumes, in order to study the infrared behavior of gluon and ghost propagators. This problem is directly related to the confinement of quarks and gluons in the physics of strong interactions.

We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each characteristic and their correlations were analyzed. A bootstrap method was applied to simulate hundreds of artificial composers influenced by the seven representatives chosen. Afterwards we quantify non-numeric relations like dialectics, opposition and innovation. Composers differences on style and technique were represented as geometrical distances in the feature space, making it possible to quantify, for example, how much Bach and Stockhausen differ from other composers or how much Beethoven influenced Brahms. In addition, we compared the results with a prior investigation on philosophy 1 . Opposition, strong on philosophy, was not remarkable on music. Supporting an observation already considered by music theorists, strong influences were identified between composers by the quantification of dialectics, implying inheritance and suggesting a stronger master-disciple evolution when compared to the philosophy analysis.