Computer network reliability in transmitting packets is studied， and a weighted directed network model of computer network is presented based on the graph theory. The network model of computer network is established according to degree， clustering coefficient and network efficiency. The degree， clustering coefficient and network efficiency were analyzed in the enterprise core network during the packet forwarding. The results show that node 5and 6 value are bigger，which has the biggest influence on network； the affinity of node 5 is biggest， which has made its greatest impact； node 5 is the core node through comparative analysis. Computer network reliability is poor during the packet forwarding through comparative analyses； and it is decided by a few important nodes.