Transmission and betweenness centrality are key concepts in communication networks theory. Based on this concept, new concepts of networkness and network surplus have recently been defined. However, all these four concepts include unrealistic assumption about equal communication between vertices. Here, we propose more realistic assumption that the amount of communication of vertices decreases as their distance increases. We assume that amount of communication between vertices u and v is proportional to d (u, v) λ where λ < 0. Taking this into account generalised versions of these four descriptors are defined. Extremal values of these descriptors are analysed.

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 λ d (u,v) where λ ∈ 0, 1 . Extremal values of these descriptors are analysed.

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