can i talk to multiple arduinos at the same time with another arduino, in a serial format?

You still are not answering the key question  - what is the maximum number of nodes in the system ?

With a parallel physical connection ANY logical topology is possible. Any device can talk and all devices have the option of listening - the only requirement is that only one device talks at a time. If one device takes the data from another, processes it and then transmits it again this is exactly the same logical effect as one node passing data directly to another node which then passes it to a third.

MK

@karim think of it like those folding plate puzzles (Rubik's magic). Many physical topologies are possible but they are still all connected using the same string (wires). Or think of squares with the same connection brought out to all four sides.

I am not even sure how this will physically work right now

If there are 6 connections to any one node, then it cant be square boards as this would only allow 4, one on each edge, once those 4 are there, your now limited to 3 for each of those boards and depending on the position some only 2 additions

If there physically "Snapping" into place then any node can go on any side and therefor any channel

a complication is identification of each node to keep then unique and routing protocols to get from one node through the network to another, this can consume large amounts of FLASH and RAM, this is why a flat bus (RS485 for example) would work better as it does not worry about that, every one can talk to everyone upto about 127 addressable Nodes

michaelkellett's point: there may be about 10 or 12 of these units, for most of experiments.

shabaz's point: I think what Peter description is the closest to what I was trying to convey.

now en considering a square, there must be 4 connections identical. I am hoping to worry about the routing problem at a later stage, where I am going to have a base unit that will pull the information by asking the units step by step and filling out a first route. if I go back to the serial comm should I create half- or full-duplex? would any of them be less costly with respect to the number of pins? I was thinking of 1/2 duplex initially, but then had the impression that i may need to have a clock signal too. Is this a valid use of two lines? other than that i think a 1/2 duplex should make more sense, am I correct?

Karim.

Vagueness is making this more complicated to explain than it needs to be. A better diagram would help for a start. And the original diagram and original post didn't specify that topology needed to be identified - does it need to be identified? Any other specifications?

Secondly, there are one-wire protocols, and of course older variants of Ethernet (think coax) didn't have a separate physical clock line either, it was a single core coax with a screen. It's up to you if you wish to have a separate clock line.

If you have all connection parallel (i.e. as Michael mentioned, i.e. folding plates game analogy) you can still have different topologies - I think this should now be clear. If it isn't clear, can you indicate this.

If you wish to identify the topology through connections  then of course you need separate connections on each side. You have the choice to have separate low speed connections as Michael mentioned, or perform it all across the connections as the one-dimensional mesh example I originally gave but extend it to two dimensions if you devise or find a suitable protocol that can avoid routing loops. You could also use four xConnect links on an XMOS device but your original question specifies Arduino. Explaining xConnect is sufficiently complicated that you'd need to study XMOS literature (on their website) I can't do it justice in a paragraph unfortunately.

The closest thing I found is here Shabaz:

AltSoftSerial Library, for an extra serial port

and this on:

https://www.arduino.cc/en/Tutorial/MultiSerialMega

Dear karim bahari, how can i do this through wireless?? please guide me.

Use a pair of ESP8266 as wireless transceivers, there probably cheaper that any other WIFI shield on the market and really easy to use.