Econophysics: physicists turned their own network tools on the stock market — and an honest note on what we actually built from it.
A correlation matrix for a large basket of shares is genuinely hard to look at directly — it's a wall of numbers, not a picture. A Minimum Spanning Tree simplifies it by keeping only the single strongest connection out to every share, but a tree can't show local clusters — groups of shares that all move together as a little clique. A Planar Maximally Filtered Graph keeps more connections than a tree while staying "planar" — drawable with no lines crossing — rich enough to actually show those clusters.
A tree forces every relationship through one single path, hiding any local structure. A dense but still-planar network keeps up to three times as many connections as a tree of the same size, while remaining something you could genuinely draw on paper without any line crossing another — a principled way to say "keep the meaningful structure, discard the noise," rather than picking an arbitrary correlation cutoff and hoping it's the right one.
MFL-PORTFOLIO-SCIENCE's Diagnostics tab shows exactly this — a "Correlation network (PMFG)" — for your loaded basket, plus the single most-connected "hub" share in it.
One honest detail worth being upfront about, exactly the same standard as everywhere else on this hub: the app does not run the literal textbook PMFG algorithm. Building it properly needs a fully general "is there still room to add this connection without crossing another line" test at every step — real graph-algorithm machinery that turned out to be genuinely hard to get bug-free from scratch. Rather than ship something whose correctness wasn't fully pinned down, MFL-PORTFOLIO-SCIENCE instead builds a different, mathematically well-understood planar network (a "stacked triangulation") that reaches the same goal — dense, planar, prioritizing your most correlated shares — by a route that's planar by construction and needs no such test at all. Same destination, an honestly different road there.
The construction MFL-PORTFOLIO-SCIENCE actually uses — start with one triangle, then keep inserting a new point inside a face and connecting it to that face's three corners — is the modern, 2000s network-science name for an idea that's genuinely over two thousand years old.
Apollonius of Perga (~240 BC) — the same ancient Greek geometer whose work on conic sections is the reason orbits are called "ellipses" and "parabolas" at all — studied what's now called the Apollonian gasket: pack a circle into the gap between three mutually-touching circles, then repeat forever into every new, smaller gap that creates. Swap "circle tangent to its neighbors" for "point connected to its face," and it's the exact same recursive instinct — fill the gap, then recurse — just wearing graph-theory clothing instead of compass-and-straightedge geometry. A 2200-year-old idea turned out to be exactly the right shape for a 21st-century correlation network.
The PMFG itself comes from Michele Tumminello, Tomaso Aste, Tiziana Di Matteo, and Rosario Mantegna, published in 2005 in PNAS — one of the more prestigious general-science journals that will publish, meaning even mainstream science recognized this as a genuine methodological contribution, not just a finance trick.
This one is a second, direct example of physics crossing over into finance, same flavor as the Wigner story elsewhere on this hub. Rosario Mantegna is one of the actual founders of "econophysics" — a real field, not a buzzword, where physicists apply the tools built for statistical mechanics and complex systems (originally meant for things like magnetism and phase transitions) directly onto financial markets. The PMFG is one of that field's most widely-used practical tools today.
A correlation network is a picture of the past, not a forecast — clusters that held together in your loaded window can and do reshuffle. It's a tool for seeing structure you couldn't see in a raw number grid, not a prediction of which shares will move together next.
General education only. Nothing here is personal financial advice or takes into account your objectives, financial situation or needs. Past performance is not a guarantee of future results.