PhD in Math @unitn and @CoMuNe Lab - FBK. Interested in Complex Networks and working on their Geometry!

by G. Bertagnolli

This is a small demo related to our (G. Bertagnolli, C. Agostinelli, M. De Domenico) recent work, *Network depth: identifying median and contours in complex networks*, arXiv:1904.05060.

Demo (it may need few seconds to load).

The Network Scientists 2010 network – download data – is a co-authorship network with nodes.

The Network Scientists 2010 network. Node colour and size depend on the Projected Tukey Depth w.r.t. diffusion distance, . Plots for and different values of $p$, the dimension of the embedding space.

Pressing the animation button `deeps`

will scale the nodes size based on the percentile they belong to. We consider the following percentiles: 99%, 97.5%, 95%, 90%, 75%, 50%, 25% and >25%. To go back, simply refresh the page!

A corpus has been built from all arxiv abstracts concerning complex network and then, through word2vec, concepts have been retrieved. We can compute similarites and distances on these words, therefore we can embed words in space.

To visualise words and relations among them, we build an undirected weighted network (thresholding the cosine similarity matrix on the 98-percentile).
In the following plot, the network structure reflects cosine similarity, node size depends on degree and node colour (`brewer.pal("PuOr")`

) on betweenness centrality.

Since the this network is built upon a thresholded cosine similarity matrix, we work directly on the matrix (without thresholds) to get the embeding of this *network of concepts* into space.

The median concepts is **dynamics**, other central words are **collective** and **behavior**.

*Network depth: identifying median and contours in complex networks*– G. Bertagnolli, C. Agostinelli, M. De Domenico– arXiv:1904.05060.- D. Edler and M. Rosvall, The MapEquation software package, available online at http://www.mapequation.org and related tutorial – data for Net. Sci. 2010
`sigmajs for R`

sigmajs.john-coene.com for interactive network plots.