The reduction in muscle force is a common symptom of several neuromuscular diseases. This phenomenon is called muscle fatigue. In normal subjects, it is generally reversible. Surface electromyography (sEMG) signals are commonly used to analyze muscle fatigue. These signals are nonlinear and nonstationary in nature. In this work, an attempt is made to analyse sEMG signals in nonfatigue and fatigue conditions using the degree distribution of visibility graphs. The sEMG signals are recorded from the upper limb muscle namely the biceps brachii during dynamic contraction with a six-kilogram load. A total of 58 subjects volunteered for the study. The signals are preprocessed, and visibility graphs are constructed. The variation in the degree distribution is studied and characterized. The results indicate that the signals recorded are complex in nature. The degree distributions are distinct between nonfatigue and fatigue conditions. In fatigue, the percentage of higher degree nodes are more. Further, the decay rate of degree is larger in the case of nonfatigue indicating the signal is comparatively random. The statistical test indicates that the features extracted are significant with a $\mathbf{p} < \mathbf{0.005}$. It appears that this method of analysis would be useful for characterizing various neuromuscular conditions. © 2018 IEEE.