Recent development of network structure analysis shows that it plays an important role in characterizing complex system of many branches of sciences. Different from previous network centrality measures, this paper proposes the notion of topological centrality (TC) reflecting the topological positions of nodes and edges in general networks, and proposes an approach to calculating the topological centrality. The proposed topological centrality is then used to discover communities and build the backbone network. Experiments and applications on research network show the significance of the proposed approach.
Evolutions of the social networks of scientific collaborations in mathematics and neuro-science were studied @cite_1 . The research result shows that the social network of collaboration network is scale-free; and, the node separation decreases with the increase of connections.
@cite_1
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We study empirically the time evolution of scientific collaboration networks in physics and biology. In these networks, two scientists are considered connected if they have coauthored one or more papers together. We show that the probability of scientists collaborating increases with the number of other collaborators they have in common, and that the probability of a particular scientist acquiring new collaborators increases with the number of his or her past collaborators. These results provide experimental evidence in favor of previously conjectured mechanisms for clustering and power-law degree distributions in networks. The co-authorship network of scientists represents a prototype of complex evolving networks. In addition, it offers one of the most extensive database to date on social networks. By mapping the electronic database containing all relevant journals in mathematics and neuro-science for an 8-year period (1991–98), we infer the dynamic and the structural mechanisms that govern the evolution and topology of this complex system. Three complementary approaches allow us to obtain a detailed characterization. First, empirical measurements allow us to uncover the topological measures that characterize the network at a given moment, as well as the time evolution of these quantities. The results indicate that the network is scale-free, and that the network evolution is governed by preferential attachment, affecting both internal and external links. However, in contrast with most model predictions the average degree increases in time, and the node separation decreases. Second, we propose a simple model that captures the network's time evolution. In some limits the model can be solved analytically, predicting a two-regime scaling in agreement with the measurements. Third, numerical simulations are used to uncover the behavior of quantities that could not be predicted analytically. The combined numerical and analytical results underline the important role internal links play in determining the observed scaling behavior and network topology. The results and methodologies developed in the context of the co-authorship network could be useful for a systematic study of other complex evolving networks as well, such as the world wide web, Internet, or other social networks. It has long been realized that social network of scientific collaborations provides a window on patterns of collaboration within the academic community. Investigations and studies about static and dynamic properties of co-authorship network have also been done in the recent years. However, the accent of most of the research is on the analysis about the macroscopic structure of the whole network or community over time such as distance, diameter shrinking and densication phenomenon and microscopic formation analysis of links,groups or communities over time. But in fact, how an individual or a community grows over time may not only provide a new view point to mine copious and valuable information about scientific networks but also reveal important factors that influence the growth process. In this paper,from a temporal and microscopic analytical perspective, we propose a method to trace scientific individual's and community's growth process based on community's evolution path combination with quantifiable measurements. During the process of tracing, we find out that it is the fact that the lifespan of community is related to the ability of altering its membership, but what's more and complementary, we find out that the lifespan of community is also related to the ability of maintaining its core members meaning that community may last for a longer lifespan if its core members are much more stable. Meanwhile, we also trace the growth process of research individuals based on the evolution of communities. Research in neuroevolution---that is, evolving artificial neural networks (ANNs) through evolutionary algorithms---is inspired by the evolution of biological brains, which can contain trillions of connections. Yet while neuroevolution has produced successful results, the scale of natural brains remains far beyond reach. This article presents a method called hypercube-based NeuroEvolution of Augmenting Topologies (HyperNEAT) that aims to narrow this gap. HyperNEAT employs an indirect encoding called connective compositional pattern-producing networks (CPPNs) that can produce connectivity patterns with symmetries and repeating motifs by interpreting spatial patterns generated within a hypercube as connectivity patterns in a lower-dimensional space. This approach can exploit the geometry of the task by mapping its regularities onto the topology of the network, thereby shifting problem difficulty away from dimensionality to the underlying problem structure. Furthermore, connective CPPNs can represent the same connectivity pattern at any resolution, allowing ANNs to scale to new numbers of inputs and outputs without further evolution. HyperNEAT is demonstrated through visual discrimination and food-gathering tasks, including successful visual discrimination networks containing over eight million connections. The main conclusion is that the ability to explore the space of regular connectivity patterns opens up a new class of complex high-dimensional tasks to neuroevolution.