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I am trying to understand how a collision occurs in Ethernet, especially when a duplex mismatch exists or when on a legacy Ethernet network two nodes transmit simultaneously.

Everyone explains the collision in an upper level (two frames collide when the one is being sent and the other is being received). However, the graph below shows that there are different circuits for Rx and Tx. How a collision can happen since there are dedicated circuits for sending and receiving frames?

Great question.

In full duplex, there is a dedicated channel for traffic from "left to right" and a dedicated channel from traffic from "right to left":

Therefore, in full duplex, collisions are impossible -- even if both NIC's transmit at the same time.

In half-duplex, however, traffic in either direction is meant to only use the wire, one direction at a time. So while physically, there is still dedicated channels, logically if one NIC receives something while it is transmitting, it logs it as a collision. The bits/signal do not actually "collide" on the wire -- a collision counter is simply incremented when the NIC is Receiving and Transmitting at the same time.

A hub is really just a powered cable that repeats every signal it receives on one interface to all the other interfaces. If two devices transmit at the same time to the receive of the hub interfaces, the hub repeats both signals at the same time to the transmit of all the other hub interfaces, and both signals received will collide at the transmit of the other interfaces, thus you have a collision where all the other interfaces have garbage signals because it is two signals at the same time.

Think of it this way, the receive of every hub interface is wired to the transmit of every other interface. Inside the hub, the transmit and receive are connected, even if they are separate at the interface.

Contrast that with a switch, where each link is terminated at the switch interface, and the switch does not have the interfaces wired together. Instead the switch has logic (usually embedded in hardware) to determine where to send frames it receives on one interface, and to prevent collisions inside the switch.

A switch is a high-density bridge. The original bridges were like PCs with multiple interfaces. You would not expect a PC with multiple interfaces to have collisions if it received simultaneous frames on multiple interfaces.

Please note that 10Base2 or 10Base5 shared the same medium, e.g. the same cable.