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Suicide is a leading cause of death among young individuals. Although early detection and intervention are vital for preventing suicide attempts, current suicide risk assessments rely heavily on clinical interviews and questionnaires, both of which are subject to patient biases. In contrast, speech analysis provides several objective advantages for estimating suicide risk. This is the focus of the 2025 SpeechWellness Challenge. This article presents a new paradigm for speech analysis based on network analyses of low-level descriptors. We evaluate the performance of this approach compared to the classical eGeMAPS+SVM model for suicide risk detection. Additionally, we assess the relevance of comparing networks derived from reading and spontaneous speech, and explore different methods for network construction, analyzing their respective performances.