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If (i_{s}=i_{1}), we call (mathcal{P}) a directed cycle.
An acyclic digraph is a digraph that has no directed cycle.
Fig. 8 a An initial network that includes a directed cycle.
If (i_{m}=i_{1}), we call P a directed cycle.
A directed cycle exists between some of its nodes, namely A→B→D→E⇔C→A.
If (i_{k}=i_{1}), we call (mathcal{H}) a directed cycle.
Similar(19)
This transformation can only take place when a cycle already exists in the initial network; TRF events cannot create directed cycles.
A weighted digraph ((mathcal{G}, A)) is said to be balanced if (W(mathcal{C}) =W -mathcal{C})) for all directed cycles (mathcal{C}).
TRF events tend to transform directed cycles into cliques, creating closely knit communities of users in which everyone is following everyone else.
This network contains no directed cycles, but a number of sink nodes (i.e., nodes with no outgoing edges; A and B in this example).
The analysis of samples from the 2010 Twitter topology shows that weakly connected groups of more than 200 400 users contain large directed cycles that include more than 80 90 % of the users.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com