On Average Distance of Neighborhood Graphs and Its Applications

Graph invariants such as distance have a wide application in life, in particular when networks represent scenarios in form of either a bipartite or non-bipartite graph. Average distance μ of a graph G is one of the well-studied graph invariants. The graph invariants are often used in studying efficiency and stability of networks. However, the concept of average distance in a neighborhood graph G′ and its application has been less studied. In this chapter, we have studied properties of neighborhood graph and its invariants and deduced propositions and proofs to compare radius and average distance measures between G and G′. Our results show that if G is a connected bipartite graph and G′ its neighborhood, then radG1′≤radG and radG2′≤radG whenever G1′ and G2′ are components of G′. In addition, we showed that radG′≤radG for all r≥1 whenever G is a connected non-bipartite graph and G′ its neighborhood. Further, we also proved that if G is a connected graph and G′ its neighborhood, then and μG1′≤μG and μG2′≤μG whenever G1′ and G2′ are components of G′. In order to make our claims substantial and determine graphs for which the bounds are best possible, we performed some experiments in MATLAB software. Simulation results agree very well with the propositions and proofs. Finally, we have described how our results may be applied in socio-epidemiology and ecology and then concluded with other proposed further research questions.

Neighborhood-based bridge node centrality tuple for complex network analysis

We define a bridge node to be a node whose neighbor nodes are sparsely connected to each other and are likely to be part of different components if the node is removed from the network. We propose a computationally light neighborhood-based bridge node centrality (NBNC) tuple that could be used to identify the bridge nodes of a network as well as rank the nodes in a network on the basis of their topological position to function as bridge nodes. The NBNC tuple for a node is asynchronously computed on the basis of the neighborhood graph of the node that comprises of the neighbors of the node as vertices and the links connecting the neighbors as edges. The NBNC tuple for a node has three entries: the number of components in the neighborhood graph of the node, the algebraic connectivity ratio of the neighborhood graph of the node and the number of neighbors of the node. We analyze a suite of 60 complex real-world networks and evaluate the computational lightness, effectiveness, efficiency/accuracy and uniqueness of the NBNC tuple vis-a-vis the existing bridgeness related centrality metrics and the Louvain community detection algorithm.

Computational prediction of Drug-Disease association based on Graph-regularized one bit Matrix completion

MotivationInvestigation of existing drugs is an effective alternative to discovery of new drugs for treating diseases. This task of drug re-positioning can be assisted by various kinds of computational methods to predict the best indication for a drug given the open-source biological datasets. Owing to the fact that similar drugs tend to have common pathways and disease indications, the association matrix is assumed to be of low-rank structure. Hence, the problem of drug-disease association prediction can been modelled as a low-rank matrix-completion problem.ResultsIn this work, we propose a novel matrix completion framework which makes use of the sideinformation associated with drugs/diseases for the prediction of drug-disease indications modelled as neighborhood graph: Graph regularized 1-bit matrix compeltion (GR1BMC). The algorithm is specially designed for binary data and uses parallel proximal algorithm to solve the aforesaid minimization problem taking into account all the constraints including the neighborhood graph incorporation and restricting predicted scores within the specified range. The results of the proposed algorithm have been validated on two standard drug-disease association databases (Fdataset and Cdataset) by evaluating the AUC across the 10-fold cross validation splits. The usage of the method is also evaluated through a case study where top 5 indications are predicted for novel drugs and diseases, which then are verified with the CTD database. The results of these experiments demonstrate the practical usage and superiority of the proposed approach over the benchmark [email protected]