"Mathematicians are really seeking to behold the things themselves, which can be seen only with the eye of the mind." This book provides the ordering of connected graphs having small degree distances. Families of graphs that are mainly considered there are trees, unicyclic graphs, bicyclic graphs and general simple connected graphs. While giving an ordering to these graphs having small degree distances results are proved dealing with the diameter in ascending order. Using these ideas trees and unicyclic connected graphs are separately ordered w.r.t the degree distance index (in increasing order). Also the lower and upper bounds on degree distance index are determined in terms of various graphical parameters like Zagreb index, order, size, diameter, radius, minimum degree, and graphs for which these bounds are attained are characterized. Besides, the ordering of trees having small general sum-connectivity index and evaluating the results for unicyclic graphs of given girth k ¿ 4 having smallest general sum-connectivity index are focused.