A class of logarithmic exponential estimators for estimating average degree of a network using triangular graph sampling

A network (graph) is used to represent complex relationships of nodes (vertices) like online social networks, air-traffic networks, pandemic spread, and other real-world networks. Graph sampling techniques are used to get a sample subset from a network to study different parameters. Many sampling algorithms like random walk, random edge, random node etc., are used for the collection of subsets of networks, but these algorithms do not sample according to the design of the network. Also, design-based efficient estimation methods are not much discussed for parameter estimation for network population. This article presents the triangular graph sampling (TGS) scheme to draw a sample and contains a proposal of a Logarithmic-Exponential (log-expo) class of estimators to estimate the average degree of a network. To collect samples, triangles of nodes are collected using randomly selected seed nodes. A comparative procedure is used to obtain the lower and upper limits of confidence interval with the help of multiple samples. An ogive-based simulation procedure is also used for single-value computation of both the limits of the confidence interval (CI). The results obtained from simulation show that the proposed TGS scheme and proposed class of estimators both provide appropriate confidence intervals that contain the true value.