High-throughput sequencing data is rapidly accumulating in public repositories. Making this resource accessible for interactive analysis at scale requires efficient approaches for its storage and indexing. There have recently been remarkable advances in solving the experiment discovery problem and building compressed representations of annotated de Bruijn graphs where k-mer sets can be efficiently indexed and interactively queried. However, approaches for representing and retrieving other quantitative attributes such as gene expression or genome positions in a general manner have yet to be developed. In this work, we propose the concept of Counting de Bruijn graphs generalizing the notion of annotated (or colored) de Bruijn graphs. Counting de Bruijn graphs supplement each node-label relation with one or many attributes (e.g., a k-mer count or its positions in genome). To represent them, we first observe that many schemes for the representation of compressed binary matrices already support the rank operation on the columns or rows, which can be used to define an inherent indexing of any additional quantitative attributes. Based on this property, we generalize these schemes and introduce a new approach for representing non-binary sparse matrices in compressed data structures. Finally, we notice that relation attributes are often easily predictable from a node’s local neighborhood in the graph. Notable examples are genome positions shifting by 1 for neighboring nodes in the graph, or expression levels that are often shared across neighbors. We exploit this regularity of graph annotations and apply an invertible delta-like coding to achieve better compression. We show that Counting de Bruijn graphs index k-mer counts from 2,652 human RNA-Seq read sets in representations over 8-fold smaller and yet faster to query compared to state-of-the-art bioinformatics tools. Furthermore, Counting de Bruijn graphs with positional annotations losslessly represent entire reads in indexes on average 27% smaller than the input compressed with gzip -9 for human Illumina RNA-Seq and 57% smaller for PacBio HiFi sequencing of viral samples. A complete joint searchable index of all viral PacBio SMRT reads from NCBI’s SRA (152,884 read sets, 875 Gbp) comprises only 178 GB. Finally, on the full RefSeq collection, they generate a lossless and fully queryable index that is 4.4-fold smaller compared to the MegaBLAST index. The techniques proposed in this work naturally complement existing methods and tools employing de Bruijn graphs and significantly broaden their applicability: from indexing k-mer counts and genome positions to implementing novel sequence alignment algorithms on top of highly compressed and fully searchable graph-based sequence indexes.