Novel topological descriptors for analyzing biological networks

Abstract

BackgroundTopological 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.ResultsIn this paper, we put the emphasis on analyzing a special type of biological networks, namely bio-chemical structures. First, we derive entropic measures to calculate the information content of vertex- and edge-labeled 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.ConclusionsOur 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.

Entropy and the Complexity of Graphs Revisited

“…In this application a measure is used together with special weighting schemes allowing for efficient classification of chemical structures with the aid of support vector machines. The same type of measure can be applied to an arbitrary weighted graph [10].…”

“…Information-theoretic measures have been used to analyze ecological networks such as food webs [8,9]. Related measures have been applied to labeled chemical structures possessing bond types and hetero-atoms [10]. In this application a measure is used together with special weighting schemes allowing for efficient classification of chemical structures with the aid of support vector machines.…”

Entropy of Weighted Graphs with Randi´c Weights

“…Following this, we introduce the concept of graph entropy for weighted graphs. We mention that Dehmer et al [48] already tackled the problem of defining the entropy of weighted chemical graphs by using special information functionals. Therefore, this paper extends the work done in [48] considerably.…”

“…We mention that Dehmer et al [48] already tackled the problem of defining the entropy of weighted chemical graphs by using special information functionals. Therefore, this paper extends the work done in [48] considerably. Another contribution of this paper relates to the study of extremal values of weighted graphs.…”

New Upper Bound and Lower Bound for Degree-Based Network Entropy

“…The basic idea was introduced in [2] as a measure of the information content for a graph and further developed as a measure of structural complexity in [3]. Afterwards, entropies of graphs and networks have been broadly used in various areas such as chemistry, biology, ecology, sociology [4][5][6][7][8].…”