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Take a look at this circuit:

enter image description here

Is it allowable to redraw the circuit like this ? Can I move cd wire until it merge with b junction ? Can I move e point like what I did in the figure ?If yes why this doesn't affect of the circuit ? Can I do this when ever I want or there is a rules,what are these rules ?

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Can I move cd wire until it merge with b junction ?

Yes, assuming the wires between c and d, and between d and b are ideal (zero) resistance (impedance) wires, because then the points c, d, and b would be considered at the same electrical potential.

If yes why this doesn't affect of the circuit ?

Because of the above stated assumption of zero wire resistance (impedance), the action does not have an affect on the circuit.

Can I do this when ever I want or there is a rules,what are these rules ?

Again yes. The rule is any points that are at the same electrical potential can be combined. You could even, if you wanted, additionally shrink the wire c-d and make it a single electrical point (node).

ADDENDUM:

This will respond to your follow up question:

How can you know If two points or more have the same electric potential ?

If there is no circuit element (resistor, capacitor, inductor, voltage source, etc.) shown connected between two points, and if it is stated (or implied because of no statement) that the wires connecting the points have zero resistance (impedance), then there can be no voltage difference (potential difference) between the two points. In the diagram at the right you could just as well shrink the wire e-f to a single point since there is no circuit element shown between the points and assuming again that the wire has no resistance (impedance).

Hope this helps.

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  • $\begingroup$ Bob D ,How can you know If two points or more have the same electric potential ? $\endgroup$ – Mohammad Alshareef May 8 at 11:25
  • $\begingroup$ @MohammadAlshareef See the ADDENDUM to my answer in response to your follow up question. Hope this helps clarify things for you. $\endgroup$ – Bob D May 8 at 11:57
  • $\begingroup$ @Bod D , Thank you so much , That's really helped alot $\endgroup$ – Mohammad Alshareef May 8 at 12:05
  • $\begingroup$ @MohammadAlshareef You are very welcome $\endgroup$ – Bob D May 8 at 12:20
  • $\begingroup$ @MohammadAlshareef So the answer is acceptable? $\endgroup$ – Bob D May 8 at 13:40

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