Question

I’m just coding a program in C++ that calculates the clustering coefficient [CC] (local and global) of an undirected graph in dot format. My problem is that the result of my program doesn’t match the output from R (with igraph library):

My program:

The cluster coefficient of "0"  is: 0.257 (88/342)
The cluster coefficient of "1"  is: 0.444 (40/90)
The cluster coefficient of "10" is: 1.000 (2/2)
The cluster coefficient of "2"  is: 0.418 (46/110)
The cluster coefficient of "11" is: 1.000 (2/2)
The cluster coefficient of "12" is: 0.667 (8/12)
The cluster coefficient of "3"  is: 0.346 (54/156)
The cluster coefficient of "5"  is: 0.571 (24/42)
The cluster coefficient of "13" is: 1.000 (12/12)
The cluster coefficient of "4"  is: 0.607 (34/56)
The cluster coefficient of "7"  is: 0.679 (38/56)
The cluster coefficient of "14" is: 1.000 (6/6)
The cluster coefficient of "15" is: 0.833 (10/12)
The cluster coefficient of "16" is: 1.000 (6/6)
The cluster coefficient of "17" is: 0.733 (22/30)
The cluster coefficient of "9"  is: 0.833 (10/12)
The cluster coefficient of "18" is: 0.714 (30/42)
The cluster coefficient of "19" is: 1.000 (6/6)
The cluster coefficient of "6"  is: 1.000 (2/2)
The cluster coefficient of "8"  is: 0.733 (22/30)

Where the “”‘s are the Nodes of the graph and the (n/m) numbers are “the links between the vertices within its neighborhood” (n) and “the number of links that could possibly exist between them” (m) respectively (description from Wikipedia)
And the output from R:

0  0.2631579        x (+2 links)
1  0.4666667        x (+2 links)
2  0.4181818
3  0.3461538
4  0.6071429
5  0.6190476        x (+2 links)
6  1.0000000
7  0.6785714
8  0.6666667        x (-2 links)
9  0.8000000
10 1.0000000
11 1.0000000
12 0.6666667
13 1.0000000
14 1.0000000
15 0.8333333
16 1.0000000
17 0.7333333
18 0.7142857
19 1.0000000

Where the first number in each row is the Node, the second is it’s local CC and the third one is my annotation when it doesn’t match my output (specifying the number of links (n) I need to add/remove to match R‘s output).

The second problem I have is that the global CC from R does not match my definition or the Wikipedia’s (unless I have misunderstood the formula). The output from R for this graph is 0.458891 and mine is 0.742

---

So I did it manually: I calculated the 8’s CC and matches my program’s output. So my question is that “is even possible that igraph library have a bug?” and if the answer is “no”: “what I’m missing?”

The graph file is this one:

graph {
  1 -- 0;
  10 -- 0;
  10 -- 2;
  11 -- 0;
  11 -- 2;
  12 -- 0;
  12 -- 1;
  12 -- 3;
  12 -- 5;
  13 -- 0;
  13 -- 3;
  13 -- 4;
  13 -- 7;
  14 -- 0;
  14 -- 1;
  14 -- 4;
  15 -- 0;
  15 -- 2;
  15 -- 3;
  16 -- 0;
  16 -- 15;
  16 -- 3;
  17 -- 0;
  17 -- 1;
  17 -- 2;
  17 -- 5;
  17 -- 7;
  17 -- 9;
  18 -- 0;
  18 -- 1;
  18 -- 2;
  18 -- 3;
  18 -- 4;
  18 -- 7;
  19 -- 0;
  19 -- 18;
  19 -- 3;
  2 -- 0;
  2 -- 1;
  3 -- 0;
  3 -- 2;
  4 -- 0;
  4 -- 1;
  4 -- 3;
  5 -- 0;
  5 -- 2;
  5 -- 3;
  6 -- 0;
  6 -- 3;
  7 -- 0;
  7 -- 1;
  7 -- 2;
  7 -- 3;
  7 -- 4;
  8 -- 0;
  8 -- 1;
  8 -- 2;
  8 -- 3;
  8 -- 4;
  8 -- 5;
  9 -- 0;
  9 -- 1;
  9 -- 5;
}

The way I calculated the CC with R is loading the graph (or generating a new one, because it can’t read dot files) into a var “f”, for example, and executing transitivity(f) for global CC and transitivity(f, “local”) for local one.

Thanks a lot for reading and sorry for my bad English.

Answer 1

One of the authors of igraph here.

I have just loaded your graph into igraph (the Python interface) and its results match yours to the last digit. Which version of igraph you are using?

As for the “global” clustering coefficient, note that there are at least two conflicting definitions:

1. Calculating the number of triangles in the entire network and dividing it by the number of possible triangles. This is the “real” global clustering coefficient, and igraph calculates this by default.

2. Calculating the local clustering coefficients for each node and taking the average. This is the “average local” clustering coefficient, and you are calculating this.