A Large Scale Analysis of Information-Theoretic Network Complexity Measures Using Chemical Structures (original) (raw)
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The first attempts to evaluate quantitatively the complexity of a system have been related to complexity of cells, organisms, and humans. Fascinated by the complex nature of the living things, a group of young mathematical biologists applied in the 1950s the Shannon theory of communications 1 to assess the information content of the living matter. 2-5 The analysis made by Rashewsky 4 provided the first proof that life on earth cannot emerge as a random event, because the probability for such an event would be incredibly small. Two different approaches have been used in defining the information content. The first one proceeded from the elemental composition of the living matter (C, N, O, etc.) and is the predecessor of what is nowadays called compositional complexity. Rashewsky' topological information has been based on partitioning the atoms in a structure according to both their chemical nature and their equivalent topological neighborhoods. Mowshovitz 6 developed further these ideas to define complexity of graphs. Minoli 7
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Background: Topological descriptors, other graph measures, and in a broader sense, graph-theoretical methods, have been proven as powerful tools to perform biological network analysis. However, the majority of the developed descriptors and graph-theoretical methods does not have the ability to take vertex-and edge-labels into account, e.g., atom-and bond-types when considering molecular graphs. Indeed, this feature is important to characterize biological networks more meaningfully instead of only considering pure topological information. Results: In this paper, we put the emphasis on analyzing a special type of biological networks, namely biochemical structures. First, we derive entropic measures to calculate the information content of vertex-and edgelabeled graphs and investigate some useful properties thereof. Second, we apply the mentioned measures combined with other well-known descriptors to supervised machine learning methods for predicting Ames mutagenicity. Moreover, we investigate the influence of our topological descriptors-measures for only unlabeled vs. measures for labeled graphs-on the prediction performance of the underlying graph classification problem. Conclusions: Our study demonstrates that the application of entropic measures to molecules representing graphs is useful to characterize such structures meaningfully. For instance, we have found that if one extends the measures for determining the structural information content of unlabeled graphs to labeled graphs, the uniqueness of the resulting indices is higher. Because measures to structurally characterize labeled graphs are clearly underrepresented so far, the further development of such methods might be valuable and fruitful for solving problems within biological network analysis.
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Journal of Mathematical Physics, 2014
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A vast variety of biological, social, and economical networks shows topologies drastically differing from random graphs; yet the quantitative characterization remains unsatisfactory from a conceptual point of view. Motivated from the discussion of small scale-free networks, a biased link distribution entropy is defined, which takes an extremum for a power law distribution. This approach is extended to the nodenode link cross-distribution, whose nondiagonal elements characterize the graph structure beyond link distribution, cluster coefficient and average path length. From here a simple (and computationally cheap) complexity measure can be defined. This Offdiagonal Complexity (OdC) is proposed as a novel measure to characterize the complexity of an undirected graph, or network. While both for regular lattices and fully connected networks OdC is zero, it takes a moderately low value for a random graph and shows high values for apparently complex structures as scale-free networks and hierarchical trees. The Offdiagonal Complexity apporach is applied to the Helicobacter pylori protein interaction network and randomly rewired surrogates.
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Here we address the challenge of profiling causal properties and tracking the transformation of chemical compounds from an algorithmic perspective. We explore the potential of applying a computational interventional calculus based on the principles of algorithmic probability to chemical structure networks. We profile the sensitivity of the elements and covalent bonds in a chemical structure network algorithmically, asking whether reprogrammability affords information about thermodynamic and chemical processes involved in the transformation of different compound classes. We arrive at numerical results suggesting a correspondence between some physical, structural and functional properties. Our methods are capable of separating chemical classes that reflect functional and natural differences without considering any information about atomic and molecular properties. We conclude that these methods, with their links to chemoinformatics via algorithmic, probability hold promise for future ...