Abstract: This paper proposes a forgotten graph topology for speech signals based on forgotten factor by applying graph technologies. Specifically， by using the Graph Fourier transform （GFT） based on the graph adjacency matrix of the forgotten graph topology， we can investigate the characteristics of speech signals in the graph frequency domain. Based on this research， we design a graph adaptive band-partitioning spectral entropy （GABSE） algorithm by extending the classical adaptive band-partitioning spectral entropy （ABSE） algorithm. Our experiments show that the performance of the proposed GABSE method outperforms that of traditional methods. More specifically， the accuracy of endpoint detection of the GABSE algorithm is 10%~20% higher than that of the traditional ABSE algorithm and the rVAD algorithm， which further verifies the effectiveness of the proposed forgotten graph for speech signals.