“I am not a self-made man. I got a lot of help,” Arnold Schwarzenegger writes in the foreword to Tim Ferriss’ book Tools of Titans: The Tactics, Routines, and Habits of Billionaires, Icons, and World-Class Performers. Schwarzenegger continues:
Like everyone, to get to where I am, I stood on the shoulders of giants. My life was built on a foundation of parents, coaches, and teachers; of kind souls who lent couches or gym back rooms where I could sleep; of mentors who shared wisdom and advice; of idols who motivated me from the pages of magazines.
From the sound of it, Arnold has a well-rounded support system, and people from all walks of life have offered him various forms of help.
For emotional comfort, professional advice, or even financial assistance, members of our support system are there for us in good times and bad. A balanced network typically includes family, friends, mentors, and colleagues, as well as professionals like therapists or coaches. Add to this list the “weak ties”—acquaintances and distant relationships—and you’ll have a diverse group of people who can help you reach your goals faster.
Do you know where your next job opportunity will come from? According to Stanford professor and sociologist Mark Granovetter, most people find new job opportunities through acquaintances rather than close friends or family. Acquaintances are more likely to connect you with opportunities simply because they move in different social circles, meaning they have access to information and networks that you wouldn’t encounter otherwise.
We’ve been using terms like “network,” “connections,” and “relationships” rather casually, but there is a mathematical discipline that describes them with the rigor they deserve and also helps us answer questions like: How strong is your network? And more importantly: How can you improve it?
Collaborate more collaboratively
One of the most prolific mathematicians in history, Paul Erdős, famously owned very few personal possessions and could carry most of them in a single suitcase. He would often arrive at a colleague’s home unannounced and stay for a few days to collaborate on mathematical problems before moving on to his next destination.
Erdős published over 1,500 papers during his lifetime—more than any other mathematician—and many of those were in collaboration with others. His work in random graph theory laid the foundation for understanding how networks evolve, a principle that can be applied to social networks as well.
The “Erdős number” is a playful measure of collaborative distance within the mathematical community. Erdős’s Erdős number is 0; if you co-authored a paper with him, yours is 1; if you co-authored with someone who co-authored with Erdős, then your number is 2, and so on. This highlights the interconnectedness of mathematicians, because, as of 2022, each recipient of the Fields Medal—often regarded as the “Nobel Prize of Mathematics”—had a finite Erdős number (with a median value of only three).
In the late 1960s, psychologist Stanley Milgram tested the hypothesis of “six degrees of separation” by asking people to send a letter to a stranger through a chain of acquaintances. Most letters reached their destination in about six steps, demonstrating that the social distance between any two individuals is surprisingly short indeed.
Building on this idea, Duncan Watts and Steven Strogatz expanded our understanding of this interconnectedness in their seminal 1998 paper on “small-world networks.” They determined that many real-world networks—ranging from social networks to neural networks—exhibit a small-world property, where most nodes can be reached from any other by a small number of steps. As Watts put it, the world is both small and clustered, and this combination is crucial to understanding how real networks function.
Use your node
“The man who does not read has no advantage over the man who can’t read,” or so goes a saying frequently attributed to Mark Twain. Similarly, it’s not enough to be well-connected; your network is only as valuable as your willingness and ability to leverage it.
The first step in building a good support network, naturally, is to put yourself on the map. A node without connections will not be reachable from any other part of the network, so the bad news for all the introverts out there is: you need to start making friends.
The kinds of friendships you build will also define the capabilities of your support system. Close friends, colleagues, and mentors are better positioned to give advice because they are privy to more context. They are also generally happier to provide support. On the other hand, connecting with a large number of people outside your immediate social circle can unlock different parts of the world, which may prove to be invaluable for finding jobs, business opportunities, or new insights.
Put simply, jazz musicians will socialize with other jazz musicians for the same reasons new parents seek each other’s company—both groups are great for sharing knowledge and resources. In fact, if you’re trying to learn new skills or continue working on existing ones, identifying hubs is usually an excellent way to get up to speed.
Building relationships with other members of these hubs can also accelerate your networking efforts. Or—even better—position yourself as a connector between adjacent groups, where members of one group don’t know anyone in the other group. This will make you indispensable in the flow of information and opportunities. Being a gatekeeper is especially effective in industries where collaboration across different fields is crucial.
Graph theory is a powerful tool for analyzing and optimizing social and professional networks, but even without pen and paper, we can usually identify the key individuals who play critical roles. Plus, the small-world effect means that even distant connections may only be a few steps away. So, if you ever need help making a dream happen, reach out to the next person who can make an introduction—any introduction, really.
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