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

16 April 2019

# New demo available! Check the network depth demo!

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.

(it may need few seconds to load).

## Network Scientists 2010

The Network Scientists 2010 networkdownload data – is a co-authorship network with $N=552$ nodes.

### Embedding in $\mathbb{R}^{15}$

The Network Scientists 2010 network. Node colour and size depend on the Projected Tukey Depth w.r.t. diffusion distance, $PTD(D_t, t, p)$. Plots for $\tau = 10$ 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! ## Words of Complex Networks

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 $N=135$ 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.

#### Embedding in $\mathbb{R}^{3}$ The median concepts is dynamics, other central words are collective and behavior.

tags: demo; - network - depth;