A network like the internet is a set of subnets that are connected to each other by a router. A router is a computer, containing multiple network devices to be connected to multiple subnets. So, it is able to forward packages from one subnet to another. A network can be represented as a graph with its routers as vertices and subnets as edges. This graph is called the topology of the network. A packet send to a host outside the own subnet usually will be send first to the so-called default router. This router (like any router) contains a table (the so-called forwarding table) with every subnet. Additionally for each net, the table contains the router through which the subnet can be reached best. So, the packet will be forwarded from router to router until it reaches the destination subnet. On this way every router looks up in its forwarding table for the best next router. A routing protocol takes care of the automatic exchange of informations between the routers to build the forwarding tables and keep them up to date. If the forwarding tables of all routers are up to date the network is called convergent. The time needed to build or update the routing tables is called the convergence time The RIP routing protocol is a well known and well explored distance vector protocol. But there are only few examinations about the convergence properties (e.g. the time needed to converge or the traffic volume produced by the routing messages). This work tries to examine a relationship between the topology properties of a network and the convergence properties of the rip routing protocol. Therefore, over 5000 single measurements were performed and statistically analyzed. Mathematical formulas have been derived from the results that are able to approximate the convergence properties of a network from its topology properties.