How can Modularity help in Network Analysis
I have a large network of routers all interconnected in a community network. I am trying to see different ways in which i could analyse this network and gain helpful insights and ways in which it could be improved just by analyzing the graph(using gephi). So i came across this measure called "Modularity" which is defined as :
to measure the strength of division of a network into modules (also called groups, clusters or communities). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules.
My question is, what can i learn by from the network by using the "Modularity" measure ? When i use it in gephi for example, the network is colored per segments but how could it be helpful ?
Answer
Modularity algorithm implemented in Gephi looks for the nodes that are more densely connected together than to the rest of the network (it's well explained in the paper they published on the website by the guy who created the algorithm - Google scholar it - Blondel, V. D., Guillaume, J., & Lefebvre, E. (n.d.). Fast unfolding of communities in large networks.)
So then when you implement this measure the colors indicate different communities determined by this algorithm and basically it'll show, in your case, which routers are more densely connected between each other than to the rest of the network.
To make this information really helpful, though, you have to juxtapose it at with at least one more measure. For instance, if you apply Betweenness Centrality measure (which shows which routers are connect the most different communities together or the most influential nodes in the network that serve as the junctions), you'd be able to identify the most vulnerable routers in every community, which should be monitored more closely. You could also filter out a community and identify the most connected routers within each community (highest degree measure), which would then show you which routers are important for that specific community.
All in all, modularity measure allows you to see vulnerable spots of your network and gives you a general idea about its structure.
There is also interesting research on modularity as the measure of network's robustness. For example, if your network has modularity that is too high, it's more robust against random external attacks, but it's also susceptible to targeted attacks on the most connected hubs (high betweenness centrality nodes). On the other hand, if it's too interconnected, you could put it down more easily if you wage a large scale attack on the routers (or if there's a blackout, for example). There's some good explanation of this in the paper (or video / slide show) on information epidemics here and a more general explanation of metastability vs modularity measure here.
Hope this helps, and let me know if you have more questions, I love this subject!