 # Easy maths question

In a network with N nodes, what's the maximum number of connections you can make?

eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc

I think it's sum of N-i from i=1 to N-1

How many when N=100?

Can I simplify this in terms of N only and what's the function called in maths and/or in Excel or google sheets?

Probably easy but it's been years since i did maths.

Thanks!
Math / Science Last Comment
hypercube

8/22/2022 - Mon
SOLUTION
Shaun Vermaak

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xenium

Thanks, I'm looking for a formula that gives the answer straight off.

Just guessing it seems to be N choose 2, that googles to the right answer for 100

Is that right?
Shums Faruk

In excel you can use below formula assuming  your data starts from A1:
``````=SUMPRODUCT(LARGE(A1:A100,ROW(INDIRECT("2:100"))))
``````
xenium

I assume we don't need arrays.

If N choose 2 is the right answer then i can just use that formula, i assume Excel has the function, else a factorial version
xenium

eg
=FACT(100)/(2*FACT(100-2))
xenium

or
=COMBIN(100,2)
xenium

Now i think about it, it all makes sense. THe number of connections is the number of ways you can choose two nodes from the whole set.
xenium

Thanks all for your input and helping me get to an answer quickly.
Shums Faruk

Why you need to send close request? right away accept Shaun's solution and it will close automatically.
hypercube

In a network with N nodes, what's the maximum number of connections you can make?

eg N=2, gives 1 connection, N=3 gives 3, N=4 gives 6, N=5 gives 10, N=6 gives lots etc

I think it's sum of N-i from i=1 to N-1
Consider this:
Starting with "n" nodes, each node added gets N nodes.
So the formula is a sum of added connections.
The number of connections is a sequence: 1,2,3,6,12,
1 to 2 adds 1 for 1 total
2 to 3 adds 2 for 3 total
3 to 4 adds 3 for 6 total
4 to 5 adds 4 for 10 total
99 to 100 adds 99 >> so we will call M=N-1 as the sequence ends at N-1
SUM over k=1:M (1:k-1) which is done with a well-known formula M*(M+1)/2
Check:
M=1>>1*(1+1)/2=1
M=2>>2*(2+1)/2=3
M=3>>3*(3+1)/2=6
M=4>>4*(4+1)/2=10
.
M=99>>99*(99+1)/2=4,950

In this case, you have to be careful because there are N nodes and N-1 added connections.  Thus M=N-1
How many when N=100?
4,950

Can I simplify this in terms of N only
Yes. As above.
what's the function called in maths
Partial sum of integers
and/or in Excel or google sheets? SUM
hypercube

xenium

Thanks Fred, that's a good point. I will request to defer closing so I can re-assign points.
xenium