  In communication networks theory the concepts of networkness and network
surplus have recently been defined. Together with transmission and betweenness
centrality, they were based on the assumption of equal communication between
vertices. Generalised versions of these four descriptors were presented, taking
into account that communication between vertices $u$ and $v$ is decreasing as
the distance between them is increasing. Therefore, we weight the quantity of
communication by $\lambda^{d(u,v)}$ where $\lambda \in \left\langle0,1
\right\rangle$. Extremal values of these descriptors are analysed.
