I did not reach a solution for the determination of **upper and lower limits** of the following function:

It applies to weighted unoriented network graphics, with *not* nodes. The formula is calculated for the node *I*. With $ alpha $ being a coefficient which can be chosen greater than zero. *wij* is the weight of the arc connection nodes *I* and *j* (with a *j* for all the neighbors in the network of *I*). The logarithm numerator represents the sum of the weights of all the arcs in the graph.

So basically we add the weights of all the arcs connected to the node *I*, by multiplying them before by the logarithmic term. Please note that for $ alpha> 1 $ the contribution of an arc to the final score can be negative.

Can you help me find a maximum and a **minimum**?

It should be expressed in terms of *not* and $ alpha $ which are fixed parameters. We also know the value of the maximum *wij*.