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.

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.

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.