Weak components of the directed configuration model

The version of record is available online at: http://dx.doi.org/10.1007/978-3-030-83823-2_109We study the threshold for the existence of a linear order weakly connected component in the directed configuration model, confirming analytic but non-rigorous results recently obtained by Kryven [8]. We also establish convergence in probability of the fraction of vertices and edges that are contained in the largest component. As a consequence of our results, we obtain that the “separation” between the thresholds for the existence a giant weakly and strongly connected component is in some sense independent from the in-/out-degree correlation. We formalise this idea using bond percolation.G. Perarnau—Supported by the Spanish Ministerio de Economía y Competitividad project MTM2017-82166-P and the MSCA-RISE-2020-101007705 - ‘RandNet’.Peer ReviewedPostprint (author's final draft