平衡k叉树网络的平均路径长度和链路效率

The average path length and link efficiency of a balanced k-ary tree

对平衡k叉树网络进行深入分析,得到n层平衡k叉树网络中平均路径长度和链路效率的精确计算公式.利用得到的计算公式,通过Matlab软件绘图,分析了平均路径长度和链路效率随网络层数n的变化趋势.得出平均路径长度是网络层数n的增函数,并且可用线性表达式近似表示;链路效率随网络层数n的增加而增加,并且趋于1.

The exact formulas computing the average path length and link efficiency of balanced k-ary tree network are given.Based on the two formulas,with Matlab drawing software,the tend-ency of average path length and link efficiency with level number n is analyzed.Average path length is an increasing function of level number n,which can be approximately expressed by a lin-ear formula.Link efficiency also increases with level number n and tends to 1 .