RESUMO
Network structures have attracted much interest and have been rigorously studied in the past two decades. Researchers used many mathematical tools to represent these networks, and in recent days, hypergraphs play a vital role in this analysis. This paper presents an efficient technique to find the influential nodes using centrality measure of weighted directed hypergraph. Genetic Algorithm is exploited for tuning the weights of the node in the weighted directed hypergraph through which the characterization of the strength of the nodes, such as strong and weak ties by statistical measurements (mean, standard deviation, and quartiles) is identified effectively. Also, the proposed work is applied to various biological networks for identification of influential nodes and results shows the prominence the work over the existing measures. Furthermore, the technique has been applied to COVID-19 viral protein interactions. The proposed algorithm identified some critical human proteins that belong to the enzymes TMPRSS2, ACE2, and AT-II, which have a considerable role in hosting COVID-19 viral proteins and causes for various types of diseases. Hence these proteins can be targeted in drug design for an effective therapeutic against COVID-19.
RESUMO
Topological indices are numerical parameters that indicate the topology of graphs or hypergraphs. A hypergraph H = ( V ( H ) , E ( H ) ) consists of a vertex set V ( H ) and an edge set E ( H ) , where each edge e ∈ E ( H ) is a subset of V ( H ) with at least two elements. In this paper, our main aim is to introduce a general hypergraph structure for the prime ideal sum (PIS)- graph of a commutative ring. The prime ideal sum hypergraph of a ring R is a hypergraph whose vertices are all non-trivial ideals of R and a subset of vertices E i with at least two elements is a hyperedge whenever I + J is a prime ideal of R for each non-trivial ideal I, J in E i and E i is maximal with respect to this property. Moreover, we also compute some degree-based topological indices (first and second Zagreb indices, forgotten topological index, harmonic index, Randic index, Sombor index) for these hypergraphs. In particular, we describe some degree-based topological indices for the newly defined algebraic hypergraph based on prime ideal sum for Z n where n = p α , p q , p 2 q , p 2 q 2 , p q r , p 3 q , p 2 q r , p q r s for the distinct primes p , q , r and s.