# Network modularity **URL:** \ **Category:** Usage\ **Tags:** R\ **Created:** [13 September 2022 09:04 UTC](https://igraph.discourse.group/t/network-modularity/1356 "2022-09-13T09:04:47Z")\ **Posts on this page:** 9\ **Page:** 1
**Author:** ![dg.aragones](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/dg.aragones/32/586_2.png) [@dg.aragones](https://igraph.discourse.group/u/dg.aragones)\ **Post date:** [13 September 2022 09:04 UTC](https://igraph.discourse.group/t/network-modularity/1356/1 "2022-09-13T09:04:47Z")
I have been exploring recently the igraph (R) documentation, because I’m interested in calculating network modularities for undirected weighted graphs. Currently, I have that calculations done in Mathematica: ```auto GraphAssortativity[G, FindGraphCommunities[G], "Normalized" -> False] ``` Is there any way in which I can calculate this (or something similar) using the R implementation of igraph? Thanks in advance for any advice. ---
**Author:** ![szhorvat](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/szhorvat/32/3_2.png) [@szhorvat](https://igraph.discourse.group/u/szhorvat)\ **Post date:** [13 September 2022 11:58 UTC](https://igraph.discourse.group/t/network-modularity/1356/2 "2022-09-13T11:58:55Z")
R/igraph 1.3 does not support calculating assortativity without normalization. This feature has been implemented in the recently released C/igraph 0.10, and will be present in whichever R/igraph is based on that (1.4 or 2.0). Until then, you would need to implement this calculation from scratch, if you need it. ---
**Author:** ![dg.aragones](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/dg.aragones/32/586_2.png) [@dg.aragones](https://igraph.discourse.group/u/dg.aragones)\ **Post date:** [15 September 2022 09:01 UTC](https://igraph.discourse.group/t/network-modularity/1356/3 "2022-09-15T09:01:43Z")
Thank you for your answer! It’s good that it will be avaible in the future. I will try to implement it from scratch, as you suggested. ---
**Author:** ![dg.aragones](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/dg.aragones/32/586_2.png) [@dg.aragones](https://igraph.discourse.group/u/dg.aragones)\ **Post date:** [21 September 2022 18:22 UTC](https://igraph.discourse.group/t/network-modularity/1356/4 "2022-09-21T18:22:34Z")
I have tried to implement it from scratch using R/igraph. This is my code using a simple example: ```auto edgelist = matrix(c(1,3, 2,1, 3,6, 4,6, 1,5, 5,4, 6,1), nrow=7, ncol=2, byrow=TRUE) # Example edge list G = igraph::graph_from_edgelist(edgelist) # Graph created igraph::E(G)$weight = c(0.1, 0.2, 0.2, 0.15, 0.3, 0.3, 0.1) # Added weights communities = c(1,1,2,2,2,2) # Example communities m = igraph::gsize(G) # Total number of edges k = igraph::strength(G) # Weighted degrees delta = outer(communities, communities, FUN="==") # 1 if same community, else 0 w = igraph::as_adjacency_matrix(G, type="both", attr="weight", sparse=FALSE) # Weighted adjacency matrix modularity = 1/(2*m) * sum((w - k %o% k / (2*m)) * delta) # Modularity ``` Using this code, I obtained `Q = 0.0401`, while in Mathematica and Python I obtained `Q = 0.0741`. I tried the first equation that can be found in the [NetworkX documentation](https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.community.quality.modularity.html). However, I haven’t obtained the same results. Do you know why this R/igraph code gives a different result? Thanks in advance for any help. ---
**Author:** ![szhorvat](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/szhorvat/32/3_2.png) [@szhorvat](https://igraph.discourse.group/u/szhorvat)\ **Post date:** [21 September 2022 19:00 UTC](https://igraph.discourse.group/t/network-modularity/1356/5 "2022-09-21T19:00:41Z")
I’m sorry, I have to correct what I said above. The non-normalized “nominal” assortativity is actually the same as modularity, just as you show in your last post. So you can use `modularity` in R/igraph. ```r > modularity(G, communities, weights=E(G)$weight, directed = T) [1] 0.09876543 > modularity(G, communities, weights=E(G)$weight, directed = F) [1] 0.07407407 ``` The default calculation is directed for directed graphs, which is what you have here. So use `directed=F` if you want undirected. The assortativity implementation in C/igraph 0.10 which I mentioned does not actually support weights. So if you need weights, then you’d have to use `modularity()` anyway. Comparison with Mathematica and IGraph/M: ```auto In[352]:= edges = Partition[{1, 3, 2, 1, 3, 6, 4, 6, 1, 5, 5, 4, 6, 1}, 2]; In[353]:= weights = {0.1, 0.2, 0.2, 0.15, 0.3, 0.3, 0.1}; In[354]:= membership = {1, 1, 2, 2, 2, 2}; In[355]:= g = Graph[Range[6], DirectedEdge @@@ edges, EdgeWeight -> weights]; In[356]:= communities = IGMembershipToPartitions[g, membership] Out[356]= {{1, 2}, {3, 4, 5, 6}} In[357]:= IGModularity[g, communities, DirectedEdges -> True] Out[357]= 0.0987654 In[358]:= IGModularity[g, communities, DirectedEdges -> False] Out[358]= 0.0740741 In[359]:= GraphAssortativity[g, communities, "Normalized" -> False] Out[359]= 0.0987654 ``` ---
**Author:** ![szhorvat](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/szhorvat/32/3_2.png) [@szhorvat](https://igraph.discourse.group/u/szhorvat)\ **Post date:** [21 September 2022 19:01 UTC](https://igraph.discourse.group/t/network-modularity/1356/6 "2022-09-21T19:01:46Z")
Regarding your code, the problems are: - `m` should be the sum of weights - There’s a mix of directed an undirected concepts. `k` is undirected because `mode='all'` was the default. `w` is directed because the graph itself is directed. Here’s an implementation of the directed version: ```r m = sum(E(G)$weight) # Total number of edges kin = igraph::strength(G, mode='in') # Weighted degrees kout = igraph::strength(G, mode='out') # Weighted degrees delta = outer(communities, communities, FUN="==") # 1 if same community, else 0 w = igraph::as_adjacency_matrix(G, type="both", attr="weight", sparse=FALSE) # Weighted adjacency matrix modularity = 1/m * sum((w - kin %o% kout / m) * delta) # Modularity ``` And undirected: ```r m = sum(E(G)$weight) # Total number of edges kin = igraph::strength(G, mode='all') # Weighted degrees delta = outer(communities, communities, FUN="==") # 1 if same community, else 0 w = igraph::as_adjacency_matrix(igraph::as.undirected(G), type="both", attr="weight", sparse=FALSE) # Weighted adjacency matrix modularity = 1/(2*m) * sum((w - k %o% k / (2*m)) * delta) # Modularity ``` ---
**Author:** ![szhorvat](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/szhorvat/32/3_2.png) [@szhorvat](https://igraph.discourse.group/u/szhorvat)\ **Post date:** [21 September 2022 19:04 UTC](https://igraph.discourse.group/t/network-modularity/1356/7 "2022-09-21T19:04:57Z")
Finally, just in case you were not aware, python-igraph is igraph’s Python interface and IGraph/M is its Mathematica interface. You can use much of the igraph functionality from those languages as well. ---
**Author:** ![dg.aragones](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/dg.aragones/32/586_2.png) [@dg.aragones](https://igraph.discourse.group/u/dg.aragones)\ **Post date:** [22 September 2022 09:21 UTC](https://igraph.discourse.group/t/network-modularity/1356/8 "2022-09-22T09:21:36Z")
Thank you so much for your time and attention. It’s weird, but I hadn’t found the `modularity()` function in the R/igraph documentation. It’s good that it’s implemented, it is very useful. Thank you also for checking my code. I see the problems now. It has been valuable for me to learn, despite being implemented at the end. Great job working on igraph, congratulations! ---
**Author:** ![szhorvat](https://yyz2.discourse-cdn.com/free1/user_avatar/igraph.discourse.group/szhorvat/32/3_2.png) [@szhorvat](https://igraph.discourse.group/u/szhorvat)\ **Post date:** [22 September 2022 12:54 UTC](https://igraph.discourse.group/t/network-modularity/1356/9 "2022-09-22T12:54:22Z")
> [@dg.aragones](#): > > It’s weird, but I hadn’t found the `modularity()` function in the R/igraph documentation. You can look for functions in the index: [igraph R manual pages](https://igraph.org/r/doc/). The documentation does need some updates and editing, but `modularity` is mostly fine.