#network theory

Every single one of us is the center of our own secret universe. We pull people into our gravity, push threats to the extreme periphery, and spin a complex web of lovers, workers, rivals, and muses around our core.

But Andy Warhol didn't just have a social orbit—he built an industrialized, star-studded, volatile multiverse that defined the trajectory of American pop culture.

Based on computational network mapping of his life span from the 1950s to the 1980s, let’s unpack the definitive anatomy of the Warholiverse. 🚀

🎨 PART 1: The Cosmic Architecture (The 4 Quadrants)

Just like our personal universes change over time, Andy’s orbit was strictly divided into four distinct geological eras, each defined by a specific color palette and cultural atmosphere:

🟨 The 1950s Commercial Art Era (Gold/Top-Right): The dawn of his gravity. Long before the soup cans, Andy was an ambitious commercial illustrator in Manhattan, building a quiet foundation with intimate romantic interests and early travel confidants

.⬜ The 1960s Silver Factory Era (Silver/Top-Left): The chaotic, explosive big bang of Pop Art. A silver-foiled industrial loft where rock stars, radical activists, and street-level eccentrics collided under high-voltage creative friction.

🟫 The 1970s Business Art Era (Bronze/Bottom-Right): The corporate restructuring phase. The birth of Andy Warhol Enterprises and Interview magazine. The open-door policy was replaced by a pristine, high-society elite, corporate accounts, and the jet-set crowd of Studio 54.

🌸 The 1980s Pop Renaissance (Neon Pink/Bottom-Left): His late-life creative rebirth. A vibrant era where Andy stepped up as a mythic godfather figure, actively mentoring and collaborating with a brilliant new generation of street-art vanguards.

📐 PART 2: The Social Taxonomy (The 5 Core Cosmic Roles)

In our own lives, we categorize people by how they affect our energy. In the Warholiverse, these roles were hard-coded into dynamic systemic structures:

💎 Diamonds (♦) = The Romantic Anchors

The real emotional substrate of Andy’s life. Because of his profound public discretion, these men held the tightest, most intimate inner radius to his personal core:

Edward Wallowitch (1950s): The foundational pre-pop love. A brilliant photographer who provided the raw images Warhol used for his famous early shoe illustrations.

Jed Johnson (1960s–1970s): The longest-running lifemate (12 years). He entered the Factory as a courier, moved in with Andy, and spent years as his dedicated caregiver after the 1968 shooting before stepping up as an interior designer.

Jon Gould (1980s): His final, deep, late-life obsession. A handsome Paramount executive who kept the romance strictly closeted from Hollywood. He is the heartbreakingly frequent emotional core of The Warhol Diaries.

📐 Squares (■) = The Factory Machinery

The operational, commercial, and physical backbones of his output. Warhol’s personal life was seamlessly linked to his production machine:

Billy Name: The literal architect of the Silver Factory. He lined the walls with tinfoil, lived in the darkroom, and curated the visual aesthetic of the 1960s.

Gerard Malanga: The hands-on producer who physically operated the silkscreen presses for the iconic Campbell’s and Marilyn prints.

Paul Morrissey: The business-minded film director who actually structured and commercialized Warhol’s avant-garde movie catalog (Flesh, Trash).

Fred Hughes: The legendary, dapper business manager who ran Andy Warhol Enterprises with a corporate iron fist throughout the 70s and 80s.

Bob Colacello: The long-time Editor-in-Chief of Interview magazine, serving as Andy’s premier high-society bridge to $25,000 portrait clients.

Steve Kaufman: The young 1980s assistant (nicknamed "Sman") who mastered the silkscreen techniques directly from the source to advance the legacy of Pop Art.

🔺 Triangles (▲) = The Catalytic Muses & Protégés

High-energy, non-romantic fixations that rapidly accelerated Warhol's artistic evolution but burned out intensely under immense psychological friction:

Edie Sedgwick (1960s): The ultimate "Poor Little Rich Girl." The silver-haired superstar who mirrored Andy’s style and brought aristocratic fashion into the underground, before burning out tragically.

Jean-Michel Basquiat (1980s): The defining late-life protege. Andy gave the young neo-expressionist street prodigy a studio and institutional validation; in return, Basquiat’s fierce brilliance taught Andy "how to paint with a brush again."

Keith Haring (1980s): The subway graffiti pioneer who viewed Andy as a pop-art deity. Andy championed his commercial ventures and guided him through the complex global art market.

Francesco Clemente (1980s): The Italian transavantgarde master who joined forces with Warhol and Basquiat for their historic, multi-layered three-way collaborative paintings.

🔮 Circles (●) & Arrows (▼) = The Cultural Nodes

The peer groups and status-symbols that provided artistic dialogue or premium public relations value:

Jasper Johns & Robert Rauschenberg: The older neo-Dada contemporaries. Their usage of everyday items heavily inspired Andy, but their relationship was complex; they initially dismissed Andy as "too commercial" and camp, pushing him to abandon painterly styles entirely for industrialized screens.

Lou Reed / The Velvet Underground: The raw sonic heartbeat of the 60s Exploding Plastic Inevitable multimedia shows.

Grace Jones & Bianca Jagger: The absolute faces of international nightlife, defining the glamorous Hollywood-meets-Manhattan celebrity shield.

Steve Rubell: The mastermind behind Studio 54, serving as the ultimate curator of the nighttime playground where Andy was a permanent fixture.

❌ The Outlier Threat Node (X) = Valerie Solanas

Every universe faces a destructive cosmic rupture. Placed on the extreme outer periphery of the 1960s quadrant is Valerie Solanas (the radical writer of the SCUM Manifesto). Her extreme distance reflects her lack of daily intimacy with the inner circle, yet her trajectory was devastating.

On June 3, 1968, feeling slighted over a lost script, she shot Andy Warhol, physically shattering his universe. The shooting permanently killed the open-door policy of the Silver Factory, replacing a free-flowing haven with locked doors, security cameras, and an underlying sense of lifetime psychological trauma.

🏁 Mind Your Own Gravity

The Warholiverse proves that a life is not a random collection of moments, but a highly structured, transactional, and emotional ecosystem. Andy curated his world like a living canvas—turning assistants into producers, lovers into safe havens, and street artists into structural revivals.

We all run our own factories. We all manage our own muses. Look at your own map: Who sits in your inner core, and who belongs on the outer boundary? 🌌🛰️

───

🚀 THE 5 STAGES OF THE WARHOLIVERSE: A Chronological Cosmic Deep Dive 🌌📊

As seen in the analytical network matrix above, a human life is not static. Our personal universes expand, contract, fracture, and recalibrate over time.

By mapping the exact geographic, emotional, and commercial coordinates of Andy Warhol's network, we can watch his universe evolve across five defining historical phases.

Let’s unpack how the gravitational pulls shifted from a lonely room in Pittsburgh to the most exclusive network in Manhattan. 👇

🟨 PHASE 1 (1928–1949): The Root & Formation Phase (Pittsburgh)

Cosmic Atmosphere: Insular, dense, and hyper-isolated.

The Gravity Center: 🖤 Julia Warhola (Mother)

The Narrative:

Following his birth in a working-class immigrant neighborhood in Pittsburgh, young Andy lives a deeply protected life. Stricken with a severe neurological childhood illness (Sydenham's chorea), he spends months bedridden.

During this period, his universe is almost entirely comprised of his mother. She feeds him Campbell’s soup, cuts out Hollywood magazine clippings with him, and fuels his initial creative escapism. At this stage, no external muses, workers, or rivals exist—it is a closed, pure, two-node ecosystem.

🟨 PHASE 2 (1950–1959): The Commercial Art Era (Early New York)

• Cosmic Atmosphere: Commercial expansion and hidden personal intimacy.

Key Addition: 🔷 Edward Wallowitch (First Major Partner)

The Narrative:

Andy breaks out of Pittsburgh and transitions to Manhattan, quickly transforming into one of the most celebrated and highly-paid commercial shoe and magazine illustrators of the 1950s. His mother moves in with him to maintain a protective domestic anchor.

For the first time, Andy opens up a sector of his universe to a romantic interest: photographer Edward Wallowitch. Operating tightly within the inner core, Wallowitch provides the literal blueprints for Warhol's art, taking photographs that Andy traces directly into his award-winning ad campaigns.

⬜ PHASE 3 (1960–1968): The Silver Factory Explosion (The Big Bang)

Cosmic Atmosphere: High-voltage creative friction, open-door chaos, total accessibility.

Key Additions: 🔺 Edie Sedgwick (Muse), 🟩 Billy Name (Architect), 🟩 Gerard Malanga (Silkscreen Producer), ❌ Valerie Solanas (The Threat)

The Narrative:

The definitive, mythic pop-art universe explodes into a silver-foiled industrial loft. Andy delegates manufacturing to his workers (Gerard Malanga on the silkscreen presses, Paul Morrissey on avant-garde film cameras). The mid-orbit is crammed with the high-society glamour of Edie Sedgwick and the raw, underground sonic heartbeat of Lou Reed.

While elite contemporaries like Jasper Johns and Robert Rauschenberg provide competitive rivalry from the upper boundaries, the open-door policy proves fatal: on June 3, 1968, outer threat node Valerie Solanas enters the orbit and shoots Andy, clinically killing his first open universe.

🟫 PHASE 4 (1969–1979): The Business Art Era (The Corporate Fortress)

Cosmic Atmosphere: Secure, calculated, commercial-elite, transactional.

Key Additions: 🔷 Jed Johnson (Longest Partner), 🟩 Fred Hughes (Manager), 🟩 Bob Colacello (Editor), 🟡 Bianca Jagger (Jet-Set), ⚫ Liza Minnelli (Pop-Culture Icon)

The Narrative:

Traumatized by the shooting, Andy permanently abolishes the open-door policy. The chaotic silver ecosystem is replaced by an iron-clad corporate office running Andy Warhol Enterprises. The radical underground is cast out, replaced by wealthy portrait clients and the elite jet-set of Studio 54. This era is defined by his deep cultural friendships with Hollywood royalty like Liza Minnelli and fashion icons, who perfectly balanced his hunger for celebrity prestige. Business manager Fred Hughes and Interview editor Bob Colacello police the commercial access lines. In his private life, Jed Johnson acts as a loyal, protective lifemate for 12 years to shelter Andy from the excessive nightlife engine of Steve Rubell

🌸 PHASE 5 (1980–1987): The Pop Renaissance (The Myth & The Mentors)

Cosmic Atmosphere: Generational mentorship, late-life revival, complete systemic equilibrium.

Key Additions: 🔺 Jean-Michel Basquiat (Core Protege), 🔺 Keith Haring (Protege), 🔷 Jon Gould (Final Love)

The Narrative:

The final, fully populated master-state of the Warholiverse before his sudden death in 1987. Andy steps into his ultimate role as a living mythic godfather of modern art. He opens up a brand-new creative quadrant (Neon Pink) to mentor the fierce 1980s East Village street art vanguard. He forms an intense, collaborative bond with Jean-Michel Basquiat, who teaches Andy "how to paint with a brush again," while guiding Keith Haring through the art market. His hidden private life is anchored by his final romantic obsession, Jon Gould, completing a magnificent, multi-layered lifelong cycle of art, labor, trauma, and gravity.

📊 The Revised 5-Phase Matrix (Including Candy Darling)To complete the picture, Candy Darling has been permanently integrated into the phase matrix. She appears in Phase 3 (Silver Era) at the mid-range, remains active in Phase 4, and completes the evolutionary masterpiece in Phase 5.

The ultimate paradox of any personal cosmos is that at the very end of a life, the entire Warholiverse collapses not because the stars fade away, but because the gravitional center itself vanishes—leaving a beautifully interconnected, glittering web of muses, lovers, and workers floating in the dark, frozen in the permanent orbit of a missing center.

Ultimately, the time will come for each of us when we, as the center of our own universe, will collapse, leaving nothing behind but the fading thought of who we were—a quiet reminder of a cosmos that once shone, even if we left no grand masterpiece in the wake of our light.

Surveillance dashboard prototype in the Zhangjiakou region of China. Including graph analysis of relationships between foreigners. https://netaskari.substack.com/p/sharp-eyes-how-to-track-a-foreigner

Which is basically Palantir ca. 2016:

vs. Palantir's dashboards from a 2022 research paper:

https://www.researchgate.net/figure/mages-of-Palantirs-platforms-from-Palantirs-Sec-filing-Palantir-2020a-134-152_fig2_362882456

And the Palantir graph building (Wikileaks 2016, via the same paper):

And Palantir's patents (2016):

The philosophy of power encompasses various theories that seek to understand the nature, sources, and implications of power in human societies. Here are some key theories in the philosophy of power:

Pluralist Theory: Pluralist theory posits that power is dispersed among multiple groups and individuals in society, and no single entity holds absolute power. According to this view, power is decentralized, and different groups compete for influence through political, economic, and social channels.

Elite Theory: Elite theory contends that power is concentrated in the hands of a small elite group within society, such as political leaders, business magnates, or cultural elites. According to this perspective, elites wield disproportionate influence over political decisions and societal outcomes, often at the expense of the broader population.

Marxist Theory: Marxist theory emphasizes the role of economic power in shaping society and maintains that power relations are fundamentally determined by class dynamics. According to Marxists, the bourgeoisie (owners of capital) hold power over the proletariat (working class) through the control of economic resources, leading to exploitation and inequality.

Foucauldian Theory: Drawing from the work of Michel Foucault, Foucauldian theory examines power as a diffuse and pervasive force that operates through disciplinary mechanisms and social institutions. Power is not solely held by individuals or groups but is embedded in societal structures and practices, shaping norms, behaviors, and subjectivities.

Feminist Theory: Feminist theories of power highlight the gendered dimensions of power relations and critique patriarchal structures that perpetuate male dominance and female subordination. Feminist scholars analyze how power operates within families, workplaces, and political systems, and advocate for gender equality and social justice.

Poststructuralist Theory: Poststructuralist theorists, such as Jacques Derrida and Judith Butler, challenge essentialist notions of power and instead focus on power as performative and discursive. Power is understood as fluid and contingent, constructed through language, discourse, and social practices, rather than being inherent or fixed.

Network Theory: Network theory conceptualizes power as emerging from relational connections and interactions between actors within complex networks. Power is distributed unevenly across network structures, with some nodes or actors exerting greater influence due to their centrality, connectivity, or resource control.

Rational Choice Theory: Rational choice theory models individual behavior as driven by rational calculations of costs and benefits, including the pursuit of power. According to this approach, individuals seek to maximize their utility or achieve their goals by strategically deploying resources and forming alliances to enhance their power position.

Critical Theory: Critical theories of power, influenced by the Frankfurt School and critical social theory, emphasize the role of ideology, culture, and social institutions in perpetuating power inequalities. Critical theorists analyze how power operates through processes of domination, hegemony, and ideological control, and advocate for emancipatory social change.

Intersectional Theory: Intersectional theory considers how power operates at the intersections of multiple axes of identity, including race, gender, class, sexuality, and ability. This approach recognizes that power relations are shaped by intersecting systems of oppression and privilege, and emphasizes the importance of addressing multiple forms of inequality simultaneously.

Introduction

Firstly, I need to explain the context of this vague question. February this year, two of my friends asked me if I would like to join their team for a math modelling competition, but then proceeded to pulled out last-minute, forcing me to do this competition with 2 strangers. Am I still cheesed? Maybe. But my teammates turned out to be amazing, so I'm happy that it worked out this way. After working non-stop for 3 days straight with little sleep, we were able to come up with a network theory approach to a data analysis problem.

I'm writing this post to organize my thoughts and explain how the connection between a .csv file and network theory was made.

The Problem

Let's say the coach of a soccer team with 30 players hands you a GIANT .csv file. This file contains EVERYTHING (passes, scores, positions of the players, when the passes were made, etc.) that happened in 38 games of the team. If you want to study how closely the players work together, how should you analyse the data given? I expect very few people would say "Network Theory". One of the cons of this approach is the fact that most of the information given must be ingnored, such as positions of the players and the time of the passes. This approach only considers who passed to who. Then, we can ask questions such as:

Who receives the most passes?

Is there a group of players that are getting all of the passes?

Definitions

Give these pages a read if you want a more in-depth explanation!

Adjacency Matrix: Wiki

Graph Theory: Wiki

Eigenvector Centrality: Wiki

Degree Distribution: Wiki

Community Graph: Wiki

A very cool paper: Network Theory and Models

The Process

To begin, I want to mention that this project was done entirely using Mathematica. I have said this once, and I will say it again: Mathematica is beautiful. Mathematica is easy to pick up due to its detailed and comprehensive documentation, while being an incredibly poweful tool. So, thank you @wolframalpha.

Back to our soccer team, I loaded the .csv file into my Mathematica notebook, and extracted the relevant data, i.e all of the passes that happened in all of the games. The next step is to count the number of passes between an abitrary pair of players. We shall order the players (in no particular order), and assign them each a number from 1 to 30. A matrix can be made, where the ij entry (row i, column j, where i,j are in between 1 and 30) is the number of passes between player i and player j. From this, we yield this heat map.

We want to look for "redder" entries, as this means this particular pair works together more often. With this information, we are able to construct an adjacency matrix for the team.

Let's try to understand this weird-looking matrix. The entry ij , tells us if there is a pass between player i and player j or not. If this entry is 0, there is NO pass and if this entry is 1, there exists a pass between these 2 players. You must wonder,

"Why are we not considering how many passes were made between them?"

We are getting to it, don't worry, but the reason why we want the binary version of the matrix is because we can create a graph. What the heck is a graph? In our context, each player is a node in our graph, and where it is placed in the picture does not matter. The adjacency matrix tells us if there is a line (an edge, if you want to be formal) in between an abitrary pair of nodes. The number of passes, acts as a weight for each node. From those assumptions, we yield this graph

This adjacency matrix enables us to turn the team into a network, whose characteristics such as the eigenvector centrality and the degree distribution (the degree of a node is the number of connections it receives) can be studied. Community graphs can also be constructed, which highlight the clusters formed within the team.

To Wrap Up

Peli Grietzer, Patterns of the lifeworld. Machine learning theory is shedding new light on how to think about the mysterious and ineffable nature of art. https://aeon.co/essays/why-poetry-is-a-variety-of-mathematical-experience

"Poetry, as the imaginative grasping of a world’s coherence, is in part ‘about’ the same thing as the scientific image: the causal-material patterns that make rational life possible. And while our scientific image in, say, the mid-20th century had nothing much that poetry could hold on to, times and images have changed – especially with the development of modern machine learning. In recent years, the field of machine learning has produced exciting mathematical and empirical clues about the patterns that make up human lifeworlds, the mechanics of imaginative grasping, and the resonance between the two."