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Mathematical modelling, analysis and computing of problems with uncertainty is one of the hottest areas in interdisciplinary research involving applied mathematics, computational intelligence and decision sciences. It is worth noting that uncertainty arises from various domains has very different nature and cannot be captured within a single mathematical framework. Molodtsov’s soft sets provide us a new way of coping with uncertainty from the viewpoint of parameterization. In this paper, we introduce the concepts of soft graphs, vertex-induced soft graphs, edge-induced soft graphs and describe some operations on soft graphs by presenting several examples to demonstrate these new concepts. Finally, we investigate some fundamental properties of soft graphs.