Add to ORKGU ovom diplomskom radu uveli smo pojam 2-grafa i konstruirali smo 2-graf pomoću određenih usmjerenih grafova te opisali osnovne pojmove i primjere vezane uz tu konstrukciju. Nadalje, definirali smo i naveli neke od jednostavnih primjera C*-algebri. Zatim smo uveli pojam C*-algebre grafova te vidjeli vezu između te algebre i 2-grafa.n this thesis we have introduced the term 2-graph, we have constructed a 2-graph by certain directed graphs and described the basic terms and examples regarding the 2-graph construction. Furthermore, we have defined and induced some simple examples of C* - algebra. Afterwards, we introduced the term C*-algebra of a graph and noticed a connection between that algebra and 2-graph