OK, I am back from holiday. I spent most of my time offline (hiking in Austria is great!) but also did quite a bit of reflection on academia and AI. I will have some things to say.
One of my intensions is to be more active on social media and I will also start a blog.
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Therefore, in practice the densest subgraph tends to return medium- to large-sized subgraphs (w.r.t. the number of nodes) but they are not very clique-like. Some works have therefore tried to modify the densest subgraph objective function to return smaller, more clique-like structures. Tsourakakis et al. [8] did this by considering the density function |E[S]|−α (|S| choose 2) which is non-negative if G[S] contains more than an α-fraction of all its possible edges. This penalizes subgraphs with a lot
of vertices and empirically we can observe that it tends to return smaller, more coherent subgraphs.](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:tnkvpa7fzk6rdtuqjcrn2pdu/bafkreih35lk6f4khg2lixzqncfeqtrwtex4k47lpibr3hfk6bxbhifntcy)
