Quantifying ideological polarization on a network using generalized Euclidean distance.

An intensely debated topic is whether political polarization on social media is on the rise. We can investigate this question only if we can quantify polarization, by taking into account how extreme the opinions of the people are, how much they organize into echo chambers, and how these echo chambers organize in the network. Current polarization estimates are insensitive to at least one of these factors: They cannot conclusively clarify the opening question.

Gromov centrality: A multiscale measure of network centrality using triangle inequality excess.

Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multiscale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess.

Nodal vulnerability to targeted attacks in power grids.

Due to the open data policies, nowadays, some countries have their power grid data available online. This may bring a new concern to the power grid operators in terms of malicious threats. In this paper, we assess the vulnerability of power grids to targeted attacks based on network science.