Filipi Nascimento Silva

Hierarchical Characterization of Complex Networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.

Quantifying the interdisciplinarity of scientific journals and fields

There is an overall perception of increased interdisciplinarity in science, but this is difficult to confirm quantitatively owing to the lack of adequate methods to evaluate subjective phenomena. This is no different from the difficulties in establishing quantitative relationships in human and social sciences. In this paper we quantified the interdisciplinarity of scientific journals and science fields by using an entropy measurement based on the diversity of the subject categories of journals citing a specific journal. The methodology consisted in building citation networks using the Journal Citation Reports® database, in which the nodes were journals and edges were established based on citations among journals. The overall network for the 11-year period (1999–2009) studied was small-world and followed a power-law with exponential cutoff distribution with regard to the in-strength. Upon visualizing the network topology an overall structure of the various science fields could be inferred, especially their interconnections. We confirmed quantitatively that science fields are becoming increasingly interdisciplinary, with the degree of interdisplinarity (i.e. entropy) correlating strongly with the in-strength of journals and with the impact factor.

Using network science and text analytics to produce surveys in a scientific topic

The use of science to understand its own structure is becoming popular, but understanding the organization of knowledge areas is still limited because some patterns are only discoverable with proper computational treatment of large-scale datasets. In this paper, we introduce a framework to combine network-based methodologies and text analytics to construct the taxonomy of science fields. The methodology is illustrated with application to two topics: complex networks (CN) and photonic crystals (PC). We built citation networks using data from the Web of Science and used a community detection algorithm for partitioning to obtain science maps for the two topics. We also created an importance index for text analytics, which is employed to extract keywords that define the communities and, combined with network topology metrics, to generate dendrograms of relatedness among subtopics. Interesting patterns emerging from the analysis included identification of two well-defined communities in PC area, which is consistent with the known existence of two distinct communities of researchers in the area: telecommunication engineers and physicists. With the methodology, it was also possible to assess the interdisciplinary nature and time evolution of subtopics defined by the keywords. The automatic tools described here are potentially useful not only to provide an overview of scientific areas but also to assist scientists in performing systematic research on a specific topic.

Investigating relationships within and between category networks in wikipedia

This work maps and analyses cross-citations in the areas of Biology, Mathematics, Physics and Medicine in the English version of Wikipedia, which are represented as an undirected complex network where the entries correspond to nodes and the citations among the entries are mapped as edges. We found a high value of clustering coefficient for the areas of Biology and Medicine, and a small value for Mathematics and Physics. The topological organization is also different for each network, including a modular structure for Biology and Medicine, a sparse structure for Mathematics and a dense core for Physics. The networks have degree distributions that can be approximated by a power-law with a cut-off. The assortativity of the isolated networks has also been investigated and the results indicate distinct patterns for each subject. We estimated the betweenness centrality of each node considering the full Wikipedia network, which contains the nodes of the four subjects and the edges between them. In addition, the average shortest path length between the subjects revealed a close relationship between the subjects of Biology and Physics, and also between Medicine and Physics. Our results indicate that the analysis of the full Wikipedia network cannot predict the behavior of the isolated categories since their properties can be very different from those observed in the full network.

A pattern recognition approach to complex networks

Complex networks exist in many areas of science such as biology, neuroscience, engineering, and sociology. The growing development of this area has led to the introduction of several topological and dynamical measurements, which describe and quantify the structure of networks. Such characterization is essential not only for the modeling of real systems but also for the study of dynamic processes that may take place in them. However, it is not easy to use several measurements for the analysis of complex networks, due to the correlation between them and the difficulty of their visualization. To overcome these limitations, we propose an effective and comprehensive approach for the analysis of complex networks, which allows the visualization of several measurements in a few projections that contain the largest data variance and the classification of networks into three levels of detail, vertices, communities, and the global topology. We also demonstrate the efficiency and the universality of the proposed methods in a series of real-world networks in the three levels.

Complex network analysis of CA3 transcriptome reveals pathogenic and compensatory pathways in refractory temporal lobe epilepsy.

We previously described – studying transcriptional signatures of hippocampal CA3 explants – that febrile (FS) and afebrile (NFS) forms of refractory mesial temporal lobe epilepsy constitute two distinct genomic phenotypes. That network analysis was based on a limited number (hundreds) of differentially expressed genes (DE networks) among a large set of valid transcripts (close to two tens of thousands). Here we developed a methodology for complex network visualization (3D) and analysis that allows the categorization of network nodes according to distinct hierarchical levels of gene-gene connections (node degree) and of interconnection between node neighbors (concentric node degree). Hubs are highly connected nodes, VIPs have low node degree but connect only with hubs, and high-hubs have VIP status and high overall number of connections. Studying the whole set of CA3 valid transcripts we: i) obtained complete transcriptional networks (CO) for FS and NFS phenotypic groups; ii) examined how CO and DE networks are related; iii) characterized genomic and molecular mechanisms underlying FS and NFS phenotypes, identifying potential novel targets for therapeutic interventions. We found that: i) DE hubs and VIPs are evenly distributed inside the CO networks; ii) most DE hubs and VIPs are related to synaptic transmission and neuronal excitability whereas most CO hubs, VIPs and high hubs are related to neuronal differentiation, homeostasis and neuroprotection, indicating compensatory mechanisms. Complex network visualization and analysis is a useful tool for systems biology approaches to multifactorial diseases. Network centrality observed for hubs, VIPs and high hubs of CO networks, is consistent with the network disease model, where a group of nodes whose perturbation leads to a disease phenotype occupies a central position in the network. Conceivably, the chance for exerting therapeutic effects through the modulation of particular genes will be higher if these genes are highly interconnected in transcriptional networks.

Concentric characterization and classification of complex network nodes: Application to an institutional collaboration network

Differently from theoretical scale-free networks, most real networks present multi-scale behavior, with nodes structured in different types of functional groups and communities. While the majority of approaches for classification of nodes in a complex network has relied on local measurements of the topology/connectivity around each node, valuable information about node functionality can be obtained by concentric (or hierarchical) measurements. This paper extends previous methodologies based on concentric measurements, by studying the possibility of using agglomerative clustering methods, in order to obtain a set of functional groups of nodes, considering particular institutional collaboration network nodes, including various known communities (departments of the University of Sao Paulo). Among the interesting obtained findings, we emphasize the scale-free nature of the network obtained, as well as identification of different patterns of authorship emerging from different areas (e.g. human and exact sciences). Another interesting result concerns the relatively uniform distribution of hubs along concentric levels, contrariwise to the non-uniform pattern found in theoretical scale-free networks such as the BA model.

Thermodynamic characterization of networks using graph polynomials.

In this paper, we present a method for characterizing the evolution of time-varying complex networks by adopting a thermodynamic representation of network structure computed from a polynomial (or algebraic) characterization of graph structure. Commencing from a representation of graph structure based on a characteristic polynomial computed from the normalized Laplacian matrix, we show how the polynomial is linked to the Boltzmann partition function of a network. This allows us to compute a number of thermodynamic quantities for the network, including the average energy and entropy. Assuming that the system does not change volume, we can also compute the temperature, defined as the rate of change of entropy with energy. All three thermodynamic variables can be approximated using low-order Taylor series that can be computed using the traces of powers of the Laplacian matrix, avoiding explicit computation of the normalized Laplacian spectrum. These polynomial approximations allow a smoothed representation of the evolution of networks to be constructed in the thermodynamic space spanned by entropy, energy, and temperature. We show how these thermodynamic variables can be computed in terms of simple network characteristics, e.g., the total number of nodes and node degree statistics for nodes connected by edges. We apply the resulting thermodynamic characterization to real-world time-varying networks representing complex systems in the financial and biological domains. The study demonstrates that the method provides an efficient tool for detecting abrupt changes and characterizing different stages in network evolution.

Concentric network symmetry grasps authors' styles in word adjacency networks

Several characteristics of written texts have been inferred from statistical analysis derived from networked models. Even though many network measurements have been adapted to study textual properties at several levels of complexity, some textual aspects have been disregarded. In this paper, we study the symmetry of word adjacency networks, a well-known representation of text as a graph. A statistical analysis of the symmetry distribution performed in several novels showed that most of the words do not display symmetric patterns of connectivity. More specifically, the merged symmetry displayed a distribution similar to the ubiquitous power-law distribution. Our experiments also revealed that the studied metrics do not correlate with other traditional network measurements, such as the degree or betweenness centrality. The effectiveness of the symmetry measurements was verified in the authorship attribution task. Interestingly, we found that specific authors prefer particular types of symmetric motifs. As a consequence, the authorship of books could be accurately identified in 82.5% of the cases, in a dataset comprising books written by 8 authors. Because the proposed measurements for text analysis are complementary to the traditional approach, they can be used to improve the characterization of text networks, which might be useful for related applications, such as those relying on the identification of topical words and information retrieval.

Knowledge acquisition: A Complex networks approach

Abstract Complex networks have been found to provide a good representation of knowledge. In this context, the discovery process can be modeled in terms of a dynamic process such as agents moving in a knowledge space. Recent studies proposed more realistic dynamics which can be influenced by the visibility of the agents, or by their memory. However, rather than dealing with these two concepts separately, in this study we propose a multi-agent random walk model for knowledge acquisition that integrates both these aspects. More specifically, we employed the true self avoiding walk modified to incorporate a type of stochastic flight. Such flights depend on fields of visibility emanating from the various agents, in an attempt to model the influence between researchers. The proposed framework has been illustrated considering a set of network models and two real-world networks, one generated from Wikipedia (articles from biology and mathematics) and another from the Web of Science comprising only the area of complex networks. The results were analyzed globally and by regions. In the global analysis, we found that most of the dynamics parameters do not affect significantly the discovery process. Yet, the local analysis revealed a substantial difference in performance, depending on the local topology. In particular, dynamics taking place at the core of the networks tended to enhance knowledge acquisition. The choice of the parameters controlling the dynamics were found to have little impact on the performance for the considered knowledge networks, even at the local scale.