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Networks (or graphs) appear as dominant structures in different domains, in- cluding sociology, biology, neuroscience and computing. In most cases, these graphs are directed which changes the semantics of the edges that are no longer symmetrical in the sense that the beginning vertex transfers some property or value to the end vertex, but not vice versa. Detecting community structure in complex networks is an interdisciplinary topic with many relevant areas of application. In order to detect communities in directed acyclic networks, apart from the direction of the edge, the requirement for topological ordering of the vertices should be taken into account. In other words, if the vertices are topo- logically order is such a way that x_1 < x_2 < ... < x_n we are interested in dividing the network into communities C1 , C2 , ..., Ck in such a way that: if x_i < x_j, x_i ∈ C_i, x_j ∈ C_j then C_i < C_j or C_i = C_j We present an algorithm derived from LPA algorithms which are commonly used in network detection, mostly because of their quick computational time and fairly good results. They were originally developed for undirected networks, but have been modified for this purpose.

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., Comment: 17 pages, 1 figure