Next-generation sequencing (NGS) technologies allow new methodologies for alternative splicing (AS) analysis. Current computational methods for AS from NGS data are mainly focused on predicting splice site junctions or de novo assembly of full-length transcripts. These methods are computationally expensive and produce a huge number of full-length transcripts or splice junctions, spanning the whole genome of organisms. Thus summarizing such data into the different gene structures and AS events of the expressed genes is an hard task. To face this issue in this paper we investigate the computational problem of reconstructing from NGS data, in absence of the genome, a gene structure for each gene that is represented by the isoform graph: we introduce such graph and we show that it uniquely summarizes the gene transcripts. We define the computational problem of reconstructing the isoform graph and provide some conditions that must be met to allow such reconstruction. Finally, we describe an efficient algorithmic approach to solve this problem, validating our approach with both a theoretical and an experimental analysis.