I don't understand what exactly VC Networks and Datagram Networks are? Could you explain the differences between these two Networks.
Without knowing the exact context for the question I'm not 100% sure if this is what you are looking for, but a virtual circuit is a network path that is established before data is transmitted and then subsequently utilized for all data thereafter until the VC is terminated. A datagram network refers to a different approach to packet transmission where each packet traverses the network on a more individual basis. A packet sent out on a datagram network may or may not take the same route as the one before or after, depending on the decisions made at each node in the network.
VC networks as X.25 or Frame Relay use a mechanism that opens a virtual channel from transmitter to receiver.
If using X.25 you want to communicate from New York to London, your communication device has to send a signal to its next X.25 switch indicating that you want to open a channel to London, and that switch sends the same signal to the following switch and so on until the signal gets to London switch.
Now that the channel is stablished the communication begins. Each frame from New York to London goes through the designated channel and when the communication ends the switches close the channel.
Datagram networks as TCP/IP don't open a predefined channel before sending the first frame of communication.
In the same example using New York and London, your device sends the first frame and the next switch will have to decide what is the best next hop for that frame and every network device will do the same until the frame gets to London.
For each frame the switch decides the best next hop so sometimes the frames will go through one path and sometimes through another.
Datagram networks are more flexible than VC networks because there is not a designated path from start to end.
I guess your question is about the difference between routing and switching. It applies on networks with inter connexion devices and the two mechanisms try to answer the question each inter connexion device ask himself : where should i transfer the information i just received.
IP is a solution based on routing. Information are grouped in packet. Each packet has a destination address and the routers (inter connexion devices in IP) treat each packet independently using the address to determine where the packet should go. It is supposed to be robust to network changes and have a better used of bandwidth resources
MPLS (or ATM) are solutions based on switching, using Virtual Circuit Identifiers (or labels in MPLS). The idea here is that you have to establish a communication path (usually using a control protocol) before any communication. After that, all the information from the sender to the destination is going to take the same path (the Virtual Circuit). Switching is supposed to be faster by lowering the need for computation in the inter connexion devices.