SIGBOVIK 2026 ✕ IETF 126 Vienna PechaKucha

Buscemi
Centrality

Source-relative centrality in heterogeneous affiliation graphs

T. E. Vaughan // T. H. Underpoot // Z. Flugelhorn

July 2026

Prior art or something

You already know the Erdős number

Your distance to a distinguished node in the coauthorship graph, compressed into a single beloved integer.

Prior art, but Hollywood yeah?

And the Bacon number

Same construction, basically, but on the film coappearance graph instead of coauthorship.

It's "six degrees of separation" but only like ½ a degree of imagination

The problem

These metrics throw almost everything away

One shortest path

All structural information collapses to a single value. Every other path you have is ignored, which is pretty wack.

All edges are equal

A handshake, a decade of collaboration, and a shared lift: identical edges and that's totally wack.

Our contribution

Buscemi centrality

A source-relative centrality measure on heterogeneous graphs with typed edges and path-quality semantics.

Named after Steve Buscemi, but he has not been informed.

The model

A graph with typed edges

G = (V, E, τ)

Vindividuals (uh, vertices)

Eedges/arcs

τ : E → 𝒯each edge gets a type, yeah?

Fig. 1: assorted cardinals, for reference.

The model

Every edge type has a price and a promise

c(t) ≥ 0

Traversal cost

How far this kind of edge carries you, whether measured in distance, effort, or awkwardness etc.

q(t) ∈ (0, 1]

Quality factor

How much "evidential strength" the interaction actually carries.

The mathematics

Path quality

Q(P) = ∏ q(t) ⁄ ( 1 + ∑ c(t) )

Multiplicative quality

One weak link drags the whole chain down.

Additive cost

Long paths pay for every hop they take.

The mathematics

Accessibility: take your best path

A(u, v) = max Q(P) over simple paths u ⇝ v

Simple paths only. “In principle one could traverse a cycle indefinitely. We have chosen not to.”

The mathematics

The source neighbourhood

Everyone within weighted radius r of the source:

Nᵣ(s) = { u : dᵤ(u, s) ≤ r }

Each member gets a weight α(u; s), proportional to its accessibility to the source. That is how strongly it belongs to the inner circle.

The measure

Buscemi centrality, at last

BC(v; s) = λ A(v, s) + (1 − λ) ∑ α(u; s) A(v, u)

λ = 1pure proximity to the source

λ = 0pure embeddedness in the source's scene

A simplification

A measure named Buscemi centrality admits only one sensible choice of source node.

s ≔ Buscemi

QED, n'est-ce pas?

Relation to prior work

It strictly generalises everything you love

1Set q(t) = 1, c(t) = 1all edges equal again, yes?

2A(v) = 1 ⁄ (1 + d)accessibility collapses to hop count

3Ranking ≡ Bacon numberwith the source set to Kevin Bacon

4Bacon ⊂ Erdős constructionso the Erdős number falls too

It follows that all of graph theory is, at some level, secretly about Steve Buscemi.

Some may argue that this is a non-sequitur, or non-constructive etc, but the authors maintain that it is axiomatic.

Worked example

John Goodman

Best path

direct coappearance

Q(P)

0.9 ⁄ (1 + 1) = 0.45

Embeddedness

0.41 across Nᵣ

BC(Goodman) = 0.43

Aside from The Big Lebowski and Monsters Inc, Goodman and Buscemi also share Barton Fink, which arguably qualifies him for the repeated_coappearance upgrade, but the authors decline to recompute, so there.

Worked example

Adam Sandler outranks John Goodman

Repeated coappearance is stronger evidence: Billy Madison, Mr. Deeds, and more, so it earns a dedicated edge type.

q(repeated_coappearance) = 0.95

0.475

A(Sandler)

0.450

A(Goodman)

≈ 0.49

BC(Sandler)

N.B.: This result is not considered a deficiency of the measure. He's made some pretty good movies honestly.

Results

Sample Buscemi centralities

Node	Best path type	A(v)	BC(v)
Steve Buscemi	(source)	1.000	1.000
Adam Sandler	direct, repeated	0.475	0.49
John Goodman	direct	0.450	0.43
Kevin Bacon	direct (Sleepers, 1996)	0.450	0.42
Harvey Keitel	direct	0.450	0.41
Paul Erdős	not established	0.000	0.000

You can calculate these for yourself if you don't believe me, and I won't mind. Paul Erdős has no path to Steve Buscemi, as far as I know.

Why you are seeing this here

The IETF edition

Buscemi Centrality Explorer, running on the IETF co-authorship graph.

Want to know your ekr centrality? Thomson centrality, or Nottingham centrality?

Datatracker, weekly

The full RFC and Internet-Draft author graph, pulled from the Datatracker API.

Anyone can be Buscemi

Pin any author who has ever written an I-D as the source node.

Live-tunable parameters

Quality, cost, radius and λ, adjustable in the browser. For science.

QR code linking to the Buscemi Centrality Explorer

the Explorer

Rankings are final, binding, and unappealable, until someone commits a new Internet-Draft, which happens on the order of hourly.

Limitations

Threats to validity

§

The measure is undefined for graphs containing no Steve Buscemi.

§

Extension to directed graphs is left as an exercise.

§

The authors have not computed their own Buscemi centrality, but assume it is non-zero.

Fin.

Paper + codegithub.com/thunderpoot/buscemi-centrality

Explorerthunderpoot.github.io/buscemi-centrality

VenueSIGBOVIK 2026 & IETF 126 Vienna

Steve Buscemi was not consulted during the preparation of this work and is under no obligation to acknowledge its existence.

You already know the Erdős number

And the Bacon number

These metrics throw almost everything away

One shortest path

All edges are equal

A graph with typed edges

Every edge type has a price and a promise

Traversal cost

Quality factor

Path quality

Multiplicative quality

Additive cost

Accessibility: take your best path

The source neighbourhood

Buscemi centrality, at last

It strictly generalises everything you love

John Goodman

Adam Sandler outranks John Goodman

Sample Buscemi centralities

The IETF edition

Datatracker, weekly

Anyone can be Buscemi

Live-tunable parameters

Threats to validity

Keys