Manlio De Domenico

Musk, worth $829 billion, owns X.

Bezos, worth $234 billion, owns The Washington Post & Twitch.

Zuckerberg, worth $231 billion, owns Facebook, Instagram & WhatsApp.

And now Larry Ellison, worth $202 billion, is about to control CNN, CBS, TikTok & HBO.

Yes, this is oligarchy.

Is “complexity” always in the eye of the beholder?

Is complexity in the system, or in the fit between the system and our description of it?

New #ComplexityThoughts:

open.substack.com/pub/manlius/...

Sadly.

Is “complexity” always in the eye of the beholder?

Is complexity in the system, or in the fit between the system and our description of it?

New #ComplexityThoughts:

open.substack.com/pub/manlius/...

💯

Evolution of methods for assessing fMRI-based functional networks: From classical pairwise connectivity to higher-order interactions The analysis of functional magnetic resonance imaging (fMRI) data has been fundamentally shaped by network science, which models the brain as a graph …

The incorrect idea that ”graphs only encode pairwise interactions“ has done a lot of damage, and will take a long time to repair.

www.sciencedirect.com/science/arti...

Quantifying biases in reconstructed brain networks Communications Physics - Network density significantly influences coefficient estimates in functional connectomes, posing challenges for consistent analysis. Here, the authors analyze multimodal...

Our featured article, February 2026: Quantifying biases in reconstructed brain networks by @comunelab.bsky.social, @manlius.bsky.social and @valedand.bsky.social
rdcu.be/e52eU

and there you go: it is a perfectly valid Hamiltonian “on a graph” in the sense of our paper, ie “graph = domain/neighborhood structure + arbitrary multivariate interaction function”.

But maybe I got it wrong, feel free to show me where/how and I will re-think about it.

/fin

Now “generic n-body” means phi_c is an arbitrary function on {±1}^n, so it has 2^n coefficients in the standard monomial basis:

9/

I can always do this on a graph, no?

Take n spins on nodes V={1,…,n}. Use the complete graph G=K_n so each node has neighborhood ∂i=V{i}.

Let the “group” be c=V and define the graph Hamiltonian by:

8/

If we truncate the expansion to order k (keeping only subsets A with |A|≤k) the number of free coefficients becomes sum_{m=0}^k binom(n,m) (minus 1 if you drop the constant).

Hyperedges don’t change this count: they only choose which c exist.

7/

Now the key distinction: “pairwise graph can’t” is shorthand for “you restrict phi_c to only |A|≤2 terms”.

But, as far as I understand, that’s a constraint on the function class, not on whether c is indexed by a hyperedge or a graph neighborhood.

6/

Let's see if I got your point.

Let a hyperedge be a set c ⊂ V with |c| = n

An “n-spin term on that hyperedge” is just a function
phi_c : {±1}^n → R, assigning an energy to each configuration of spins in c.

So far so good?

5/

Hyperedges don’t fix the “2^n dof” issue.

A generic n-spin term is an arbitrary function on {±1}^n, i.e., it has 2^n values (well, minus a constant gauge).

Here’s the count in a standard basis: any n-spin potential expands over all subsets, 2^n coefficients (again, minus the constant term).

4/

But that “cannot” is about this specific choice of potential (sum of 1-body + 2-body terms), not about graphs as neighborhoods/domains.

A graph can still parameterize who can influence whom while allowing multivariate couplings on neighborhoods (the point of our paper).

3/

If by “graph” you mean (ie, assume by design) the pairwise Ising restriction, then you’re right: that family cannot represent a generic n-body interaction on the same spins.

To be clear, I am referring to the Hamiltonian below. Which is, btw, a specific “mechanism choice”, not a structural one.

2/

How hypergraphs would avoid the O(2^n) dof of a generic n-body Ising term?

They only index which subsets get a term: if graphs specify neighborhoods/domains and node interactions are arbitrary multivariate functions on them, hypergraph models are a constrained subfamily.

1/

The Slow Science Movement advocates for a more thoughtful, sustainable approach to research that values quality over quantity and depth over speed.

It sounds trivial, but if you are an active researcher you know it is not.

👉 www.slow-science.com/index.html

It seems to me that the point about being "true" or "intrinsic for" or "more general than" has been done in other 100s papers.

The point is about "telling the truth" and being counterfactual, not claiming what's "true", since there is no such a thing as a "true" model, by definition.

I think it's a legit question and, actually, something I agree with.

If social media were not important to influence human behavior, why so much investment on them?

A possible answer is also: just because they made platform richer.
But very legit doubt.

The evolution of cheaper workers facilitated larger societies and accelerated diversification in ants Ants rose by favoring the power of many over the might of few.

“Our results support a hypothesis whereby evolving cheaper but more numerous units through reduced investment in structural tissues was a strategic trend in the evolution and diversification of complex insect societies”

🧪🌐🐜

www.science.org/doi/10.1126/...

Partially agree: there is at least one study supporting this and I can't find studies supporting the opposite.

I am fine with being cautiously confident and waiting for more results.

@acerbialberto.com what's your take on this?

I remember we had several discussions where you were sustaining the opposite, ie that social media have no influence.

The political effects of X’s feed algorithm - Nature Among users initially on a chronological feed, 7 weeks of exposure to X’s algorithmic feed in 2023 shifted political attitudes and account-following behaviour in a more conservative direction compared...

“initial exposure to X’s algorithm has persistent effects on users’ current political attitudes and account-following behaviour, -even in the absence of a detectable effect on partisanship”

That's the reason for a large body of research in the last two decades.

www.nature.com/articles/s41...

Using hypergraphs for your data?

Believing that hypergraphs “generalize” standard graphs to “higher order” structures?

Maybe you are conflating structure with mechanism, and this podcast is for you!

🎧 Spotify: creators.spotify.com/pod/show/com...
🎧 Apple: podcasts.apple.com/us/podcast/c...

Russell, in 1916, in the preface of his book (and also throughout the book) was distinguishing form (ie, morphological structure) and function: archive.org/details/form...

His “form” is geometric/anatomical (ie, spatial organization), but in our term that's similar to “structure” (ie, adjacencies).