Due to the advancement of our information society the underlying network infrastructure has gone beyond a certain limit that its maintenance is becoming more and more difficult to accomplish. The increase in numbers of network devices and their connections resulted in such network structures that troubleshooting has become a time-consuming and expensive task. As a result it has become necessary to automatically discover the topology of the network using computer algorithms. The work regarding my thesis has been done at a Hungarian software developer company, NETvisor Ltd., where I developed two separate algorithms for this task. The first one is based on the proprietary CDP protocol by Cisco Systems and it presents an easy way to discover network topology among Cisco devices. The other algorithm is based on the Simple Network Management Protocol (SNMP) and as a result is vendor-independent. Both have been developed in the context of a Java application and their testing has been done at the experimental network of NETvisor Ltd. At the end of my thesis I compared these to algorithms and conducted time trials to measure performance.