Context. To understand the formation, evolution, and present-day properties of the cosmic web we need to study it at low and high redshifts. Aims: We trace the cosmic web at redshifts that range from 1.0 ≤ z ≤ 1.8 by using the quasar (QSO) data from the SDSS DR7 QSO catalogue. Methods: We apply a friend-of-friend algorithm to the quasar and random catalogues to determine systems at a series of linking length and analyse richness and sizes of these systems. Results: At the linking lengths l ≤ 30 h-1 Mpc, the number of quasar systems is larger than the number of systems detected in random catalogues, and the systems themselves have smaller diameters than random systems. The diameters of quasar systems are comparable to the sizes of poor galaxy superclusters in the local Universe. The richest quasar systems have four members. The mean space density of quasar systems, ≈ 10-7 (h-1 Mpc)-3, is close to the mean space density of local rich superclusters. At intermediate linking lengths (40 ≤ l ≤ 70 h-1 Mpc), the richness and length of quasar systems are similar to those derived from random catalogues. Quasar system diameters are similar to the sizes of rich superclusters and supercluster chains in the local Universe. The percolating system, which penetrate the whole sample volume appears in a quasar sample at a smaller linking length than in random samples (85 h-1 Mpc). At the linking length 70 h-1 Mpc, the richest systems of quasars have diameters exceeding 500 h-1 Mpc. Quasar luminosities in systems are not correlated with the system richness. Conclusions: Quasar system catalogues in our web pages and at the Strasbourg Astronomical Data Center (CDS) serve as a database for searching superclusters of galaxies and for tracing the cosmic web at high redshifts. Appendix A is available in electronic form at http://www.aanda.orgThe catalogues are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/568/A46