Knowledge of the up-to-date network topology (i.e. Layer 2 & Layer 3) is crucial for efficient network management. Issues like congestion avoidance, resource management, resource discovery, root-cause analysis and event correlation require accurate information of the topology map. Due to dynamic nature of today?s IP networks, keeping track of topology information manually is a daunting task. Thus efficient algorithms for automatically discovering physical network topology are necessary. The earlier work has typically concentrated on discovering topology either using completely SNMP-MIB or ICMP echo request/reply, DNS, Trace route, etc. Our proposed algorithm does not rely totally on SNMP-MIB information as it is not usually supported by all devices in the network. Instead we propose an approach where SNMP agent should only be enabled on the routers and managed switches. Rest of the network computers/hosts need not have SNMP agent enabled. We propose an efficient algorithm not only to find available computers/hosts but also to find appropriate timeouts and delays in the network. The experimental results validate our approach, demonstrating that our algorithm discovers accurate physical topology.