# The ‘Small World Theory’ of going viral

Why are L.L. Bean duck boots, a product that’s been around for 100 years, suddenly everywhere? The retailer will sell 500,000 pairs this year, up 3x from a few years ago. Kanye West just launched his own brand of the footwear. Marketers trying to “go viral” in today’s world of social media likely understand the basic dynamics of seeding conversations among influencers. But one model often neglected is how ideas that completely oppose each other — say, Hillary Clinton vs. Donald Trump, or rubberized Maine boots donning the feet of New York City hipsters — often collide in networks to surprising effects.

Let’s start first with how things spread in social networks. In 1990 John Guare wrote the play “Six Degrees of Separation,” later made into a movie with Will Smith, which theorized everyone in the world is connected via relationships in only six or fewer steps. Put the right idea in the right network connection, and that idea might spread to everyone. The theory was made more popular by Malcolm Gladwell’s writings and the movie game “Six Degrees of Kevin Bacon” (think of a film with Kevin in it, his other actor, and you’ll likely connect that second actor to any other actor if you’re clever, ’cause Kevin gets around…).

As social media emerged, this theory was one of several others — including Robin Dunbar’s rule of 150 relationships, Metcalfe’s law of network value, and Zipf’s law that things in series always follow in statistical diminishing value — that helped marketers understand how things spread virally online.

The mathematical formula for going viral

The idea of “going viral” actually has a basic mathematical model. Ideas, or “memes,” spread when the passalong rate exceeds the absorption rate of each next node, multiplied by the cycle time. This basic formula for “going viral” …

Viral spread = (Message generation rate — Absorption rate) *Cycle time

is used by companies such as Symantec and organizations like the Centers for Disease Control and Prevention to predict when digital or biological viruses will scale to the masses.

But there is an important second part to network theory, which explains why ideas seem to replicate and also run into their polar opposites at the same time in human networks.

The Small World Theory

In June 1998, researchers Duncan Watts and Steven Strogatz published a letter in Nature called “Collective Dynamics of ‘Small-World’ Networks.” They analyzed biological, technical and social networks and found a paradox in almost all network connections: While individual “nodes,” such as humans on a computer, tend to cluster in groups of similar beings, even tightly knit network groups tend to have a few links that shoot out to another clustered group somewhere. It only takes a few of these distant links to collapse the overall network into a “small world,” where ideas or viruses or memes from one clustered population can rapidly spread to another. Imagine, a community is hit with a bad flu virus, and then just one person gets on a plane. Or you share a funny story about Donald Trump or Hillary Clinton, and suddenly one Facebook friend gets upset. Watts and Strogatz called this near-and-yet-far propagation the Small World Theory.

We see this dichotomy in our U.S. presidential race (Donald Trump vs. Bernie Sanders supporters applauding each other while yelling at others), in our broader media ecosystems (Fox News vs. MSNBC information bubbles, often reacting to what the other side says), and even in our global political tribes (Western liberalism vs. ISIS conservatism, a fight that The Atlantic recently reported is largely based on the perceived role of women in society). What one group considers normal is validated by others in close proximity, but the idea is shared across a long connection to another group who may despise the same idea.

For marketers, this Small World Theory has big implications, because occasionally an idea loved by one community can break through to another via these random long connections. Think of today’s fad for L.L. Bean duck boots, which are now running out of stock due to college-student demand; or the surge in beards among all U.S. males started by a few hipsters for a November “Movember” cancer-awareness stunt, harming razor blade sales. Small led to big, and somehow, big adapted.

Because ideas spread from close homogeneous groups first to different-interest groups second, a marketer must rethink her strategy to two stages. First, an idea should not only resonate among the product’s closest fans or prospects, but also be able to influence a different population at the second stage, when it is boosted via long-network links to groups outside the core audience. If both stages can be achieved, the marketing idea will then truly scale. The ideas with the greatest sticking power — today’s major religions — have followed this dynamic.

As James Gleick wrote in his masterful book “The Information,” “the network has a structure, and that structure stands upon a paradox. Everything is close, and everything is far, at the same time.” Networks are built to replicate the ideas we love among those nearest us, and at the same time, send our ideas into orbit among others who don’t understand how we think at all.