Some really interesting "composition networks" showing musical transitions through a song by Niccolo di Marco, @walter4c.bsky.social and others. I love how Autumn Leaves is so much denser than everything else. arxiv.org/pdf/2501.07557

I'm on the job market! I graduate with my PhD in network science this April, seeking a postdoc in Atlanta or remote. I work on theoretical and data-driven problems under Albert-László Barabási. I love being the "math guy" on interdisciplinary teams. Want help studying networks? Please reach out!

And this approach works really well! Because these nodes are both weak and well-connected, they can prevent a cascade before it's too late and better than many existing algorithms!

7/7

The critical set (green nodes) is the set of nodes they argue to protect. These nodes are both are fragile, implying they are not resilient to attacks. Secondly, these nodes have degree larger than the critical degree, implying they are well-connected enough to potentially start a cascade.

6/7

Using graph coloring, the authors successfully identify these fragile nodes. Graph coloring is a concept that stems from the 1800s. Graph coloring consists of assign each node a color such that each node does not share the same color as it's neighbor. (Image Wikipedia - Graph Coloring).

4/7

Cascading failures in a network are when the failure of a small fraction of nodes leads to the failure of the network as a whole. It is essentially a domino effect that quickly ceases a network's function. For example, a power grid failure may lead to a region-wide blackout.

2/7

Belated update: I’m officially a PhD candidate! I proposed my dissertation on how local connection rules shape the global structure of complex systems. I’m developing new network models and metrics to understand this phenomena using tools from statistical inference to knot theory. Excited to dig in!

My personal favorite is looking at the strong, repeat relationships in the network. While most nominees only collaborate once or twice, a few work together over and over again. Scott Pask, nominated for scenic design, and Christopher Gattelli, nominated for direction, have worked together the most.

Things change ever so slightly when we examine betweenness centrality, a measure of how much the nominee connects a random pair of nominees. Here a few performers and creatives become slightly more important. Notably, Gabriel Ebert, nominated as a featured actor in a play, jumps up in the rankings.

Interestingly, performers and creatives don't stand out in terms of number of connections. In fact the most connected nominee is sound designer, Dan Moses Schreier, nominated for the musical revival of Floyd Collins.

In honor of the @thetonyawards.bsky.social tonight, I made a Tony award nominee network! Nominees are connected if they collaborated in a Broadway or Off-Broadway Show up to the '21-'22 season. Gold = Performer / Blue = Creative / Red = Other. #tonyawards #networks

🧵 of network stats for the nerds