Extremal problems on exponential vertex-degree-based topological indices.

In this work we obtain new lower and upper optimal bounds for general (exponential) indices of a graph. In the same direction, we show new inequalities involving some well-known topological indices like the generalized atom-bound connectivity index $ ABC_\alpha $ and the generalized second Zagreb index $ M_2^\alpha $. Moreover, we solve some extremal problems for their corresponding exponential indices ($ e^{ABC_\alpha} $ and $ e^{M_2^{\alpha}} $).

Normalized Sombor Indices as Complexity Measures of Random Networks.

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

Complex Network Study of the Immune Epitope Database for Parasitic Organisms.

BACKGROUND: Complex network approach allows the representation and analysis of complex systems of interacting agents in an ordered and effective manner, thus increasing the probability of discovering significant properties of them. In the present study, we defined and built for the first time a complex network based on data obtained from Immune Epitope Database for parasitic organisms. We then considered the general topology, the node degree distribution, and the local structure (triadic census) of this network. In addition, we calculated 9 node centrality measures for observed network and reported a comparative study of the real network with three theoretical models to detect similarities or deviations from these ideal networks. RESULT: The results obtained corroborate the utility of the complex network approach for handling information and data mining within the database under study. CONCLUSION: They confirm that this type of approach can be considered a valuable tool for preliminary screening of the best experimental conditions to determine whether the amino acid sequences being studied are true epitopes or not.

The application of molecular topology for ulcerative colitis drug discovery.

INTRODUCTION: Although the therapeutic arsenal against ulcerative colitis has greatly expanded (including the revolutionary advent of biologics), there remain patients who are refractory to current medications while the safety of the available therapeutics could also be improved. Molecular topology provides a theoretic framework for the discovery of new therapeutic agents in a very efficient manner, and its applications in the field of ulcerative colitis have slowly begun to flourish. Areas covered: After discussing the basics of molecular topology, the authors review QSAR models focusing on validated targets for the treatment of ulcerative colitis, entirely or partially based on topological descriptors. Expert opinion: The application of molecular topology to ulcerative colitis drug discovery is still very limited, and many of the existing reports seem to be strictly theoretic, with no experimental validation or practical applications. Interestingly, mechanism-independent models based on phenotypic responses have recently been reported. Such models are in agreement with the recent interest raised by network pharmacology as a potential solution for complex disorders. These and other similar studies applying molecular topology suggest that some therapeutic categories may present a 'topological pattern' that goes beyond a specific mechanism of action.

A study of the Immune Epitope Database for some fungi species using network topological indices.

In the last years, the encryption of system structure information with different network topological indices has been a very active field of research. In the present study, we assembled for the first time a complex network using data obtained from the Immune Epitope Database for fungi species, and we then considered the general topology, the node degree distribution, and the local structure of this network. We also calculated eight node centrality measures for the observed network and compared it with three theoretical models. In view of the results obtained, we may expect that the present approach can become a valuable tool to explore the complexity of this database, as well as for the storage, manipulation, comparison, and retrieval of information contained therein.