Sunday, 8 June 2014

Analogies between interconnected and clustered networks

Indiana University
School of Informatics and Computing

VIDEO

Overview: In this talk, I will illustrate how spectral methods can be used to determine common properties shared by interconnected networks and graphs with community structure. In particular, I will show that degree correlations play a fundamental role for the characterization of the structural phases of these systems.

Radicchi, F (2014) Driving interconnected networks to supercriticality Phys. Rev. X 4, 021014
Radicchi, F (2013) Detectability of communities in heterogeneous networks Phys. Rev. E 88, 010801(R)

1. Small question: at the beginning of your presentation you showed a graph of tennis players. Why was this a directed graph? If player A plays player B [so edge(A,B) exists], it is always the case that player B plays player A [so edge(B,A) exists] as well. Right?

1. Hi Rachel,
directions indicate the outcome of matches. A beats B is represented as B -> A. Edges are also weighted. If A beats B n times, then the weight of B -> A equals n. Note the reverse edge A-> B exists only if B beats A. If you apply this recipe to a certain amount of data (for example all matches of the year), you can construct a weight and directed network of contacts among tennis players. I used this type of networks to measure the "performance" or "prestige" of players with an algorithm similar to pagerank. Details and results are published in http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0017249 .

2. Comment calcule-t-on la probabilité d'être dans une sous-couche de réseau A ou B? Je n'ai pas saisi ce bout.

Translation : How do you calculate the probability of being in layor A internetwork or layor B internetwork?

1. In the model, the number of intra- and inter-layer edges are the same in both layers A and B. This means that the probability of being in one layer is equal to 0.5.

3. Very interesting talk! My first question for Professor Radicchi concerns his method for individuating networks in terms of dense interconnectivity and random walks. Contrast this with Professor Nishikawa’s analyses, which individuate structural clusters not in terms of interconnectivity but in terms common structural properties among nodes. How is this approach related to your own?
My second question concerns the robustness of networks in cases of catastrophic cascades. Are there any particular meta-network properties that safeguard, or help protect, a network of networks from cascading catastrophes?

1. The method presented splits the graphs into different clusters with a variation of the minimum cut method (see http://en.wikipedia.org/wiki/Minimum_cut).
The method presented by Prof. Nishikawa looks at other properties and i more general. There are no simple analogies between the two methods.

Intuitively, you can expect that the multilayer network is a safe state when is indistinguishable from a non layered network, and subjected to catastrophic failures when in the decoupled or bipartite phase.

4. This question may be basic or naive, but I didn't exactly understand the difference between a "well-defined" network vs an "ill-defined" network. What characterizes each one? Are dynamics taken into account? Is it just based on interconnectivity or do structural properties are taken into account too? What's the role that "detectability plays in all this" I got a little lost. Can you give a real-life example in which you can differentiate between the two (ill defined vs well defined)?

1. Ok, so now I see that the ill-defined have more connections outside than inside the comunity. Still, how is this related with detectability? I still haven't be able to understand that.

2. The typical definition of a community is a group of nodes with a density of internal connections than the density of external connections. If each node in the community has more connections inside than outside, then this can be viewed as a "well-defined" community. If the former is not true and many nodes have more connections outside than inside, then this group can be viewed as an "ill-defined" community.

5. Networks modeling with random variables is a probabilistic approach. What’s would be main differences, advantages, inconveniences of networks modeling with a possibilistic fuzzy approach? Fuzzy network modelling is more easy to interpret and communicate?