What shape is your network? You’re wrong

What shape is your network? Do networks have shapes? People seem to think so. They’re referred to as “topologies” and you see the same sort of mentality in organisational charts. Similarly, your organisation’s org chart is lying to you. A blatant lie. It draws a picture — a graph of arrows and nodes, or vertices and edges — people believe it, yet it’s wrong. The topology of most organisations is a top-down hierarchy, in which the power is centred at the top and commands are passed down through levels of control and authority lower and lower reaching the workers at the bottom. On the “factory floor” or the “sales force” or “front line”. Whichever analogy describes best the people who spend all their time doing the applied work and none of their time commanding (or “managing”) subordinates. This is still a dominant topology for many organisations other than the very young startups, which pretend to be flat and equal, and the very trendy, which pretend to be informally mixed up and organically interconnected and equal, man. However, if you draw out the org chart of any organisation, it is a deceptive lie. Your org chart is lying to you.

Who is connected to who? The traditional and expected way of viewing this is by authority. Who can issue commands to who, who can sack or promote who, who pays who. Another way of viewing the situation is by who influences who, and viewed this way the connection graph looks totally different. Some people in an organisation are not influential at all. Even at the top. There are people at the top of an organisation that few even recognise as working there, most people don’t attach their name to their face, and what function they perform is a mystery. If they have any influence at all, it’s a generally vague ‘fear’ experienced from a distance instilled by association with certain offices that most people don’t go near. Apart from that quiet background-level impression, they have no specific influence at all. You can almost ignore those people. Without them, life would not be detectably different. However, your organisation’s traditional-style org chart is simply a map of fear — that’s all it is.

Then you have people at the top who everybody knows — their name, their aim, their personality — and although any interaction with them is definitely one-sided (they own the company, or can sack you, or promote you) it is at least reassuringly predictable and not such a mystery. You kind of know where you stand with those people, you know enough about them to transact usefully. They’ve publicised or made known all of the necessary information about themselves over the course of time as a social investment. However, it may often prove to be that the most influential people in an organisation, and therefore, where the most dynamic transactional value activity in the network takes place, is not at the top. It’s elsewhere, and could be anywhere — it doesn’t relate to your accepted org chart at all. We’re beginning to glimpse a different network graph altogether.

There are popular nodes in a network, and these become even more popular because they offer the richest connections to the most other nodes in one easy action. The people that everyone knows, the gossips through who all traffic travels. The people who act as interfaces between all the departmental networks in the organisational environment. Not just the hubs within the departments, but the circuses that connect the different departments and even the outside world.

Who sees everybody in the organisation? Who interacts with everybody? Not just a casual “hello” and “goodbye” but a useful transaction offering value, that bridges domains. Who are the circuses? These are often also the influencers. If they get a new type of phone, or wear a new fashion item, or use a new app, ride a new type of bike, or read a new book, or shop online through a certain site, or have their hair in a certain way, soon a few more people align themselves with these choices. Many people within and connected to the organisation gain value from these people who influence, and they afford credibility and reputation to these influential highly connected circuses. However, you won’t see any of that on an org chart. Essentially, if you’re an owner or founder or some other chief of an organisation and you think you’re the boss because you’re in the top area of your org chart, there’s a fair chance you’re wrong. Your  org chart is actually a map of fear, and it’s been lying to you all along.

Your morsels of value

What do I mean by network value? In a network, the popular nodes become even more popular, according to a “rich get richer” fashion known as “Preferential Attachment”. Previously I have used the example of the London Underground, although that is not a particularly good example in terms of dynamics, because the popular stations are interchanges. There is very little occasion for a new interchange to suddenly pop up at a station that hitherto was not an interchange. New stations don’t materialise that often, so the whole analogy proves a bit slow to visualise in action.

The network value of a vertex in a network, which is rewarded by affordability of opportunity to increase connections in a scale-free manner, is itself a complex parameter. What do I mean by value? Up to now, we’ve just been assuming we mean that we offer something, perhaps something unique or perhaps something appreciated or liked or funny or thoughtful or provoking or some other appealing lure. If a node in a network produces something no other node does, and if as coincidence would have it, other nodes in a network actually appreciate that product, then that’s what we’ve been imagining what I mean by “value” within a network. But this is quite subjective.

Lots of nodes, sorry, people, produce and present to the network more or less nothing. When they do, it might be of low importance such as mentioning that their cat rolled over. Or it might be something derived that they are simply passing on, like a retweet or a pasted-in motivational quote. Motivational quotes are a freely utilised currency. As far as I’m aware, Henry Ford, Bob Marley and Thomas Edison don’t actually have twitter or facebook accounts, what with the inconvenience of being dead and all that. Yet much of what they ever said in their lives is passed around freely. Not only as a way of cheering people up (or ‘motivating’ them), but packaging it as a kind of “you got that good feeling from me” emotional transaction.

As I say, a node that produces is not always offering value to the network. In a work environment, if someone farts, the value of their unique production is generally not appreciated or liked, nor does it give everyone else a good feeling. So you see, it’s subjective. What we consider value is often measured and quantified in terms of a qualitative effect on us. The more happy it makes us, the more value we assign to that direct contact on the network that packaged their output into tiny little morsels, nibble after nibble. We afford network fitness to them as a reward. But only if we calculate that they offer value to us, and this is purely in terms of how good it makes us feel at the time. It’s all very much instant gratification, there’s almost nothing long-term about this, and it doesn’t correlate with any true usefulness of the information, just how sweet it tastes to us.

Drowning in social networking

Who are all these people subscribing me or following me or whatever? I don’t know them and they don’t know me. The most they can possibly know about me is from my picture, profile and a quick look at the latest stuff I posted or tweeted or the videos on youtube that I make. None of those followers know what kind of a person I really am, nobody knows anything much about me unless you’re a long-term friend. However we all need to expand our connections, but the vast majority of those we connect to will turn out to be passively useless. Of course, you have no idea which ones those are, because someone connected to you may seem to be contributing nothing but they in turn may connect to someone else who connects to someone else, who, well, you get the idea. Distant and weak links are often valuable. Not all the time, but it happens.

The point is, these social networks are actually directed graphs, even though it doesn’t seem like it. There are people who tweet out or post out. There are people who don’t, or hardly ever, or when they do it’s about something mundane in their life such as their cat looking cute again. There are people who read these messages and people who ignore most of them. When you have a lot of followers and in turn you follow a lot, you can’t possibly spend all day reading it all, you’d get nothing done. Some people produce content on the social networks, some people consume content, some redirect, retweet or repost and act as hubs within their own networks. Some even act as circuses linking the hubs that they pay attention to, at the expense of discrete islands of nodes.

Therefore some information is going out from many nodes, some information is coming in to many nodes, and not all nodes balance this equally. The network value of a node is related to how actively it will process from input to output usefully to others (either reading it, or retweeting it, etc). If it does nothing, or just occasionally posts about the cat, it’s effectively just noise. However, as I stated, you can’t just remove all the first degree connections that seem useless, they may be connected further away to someone more useful —you simply never know.

A lot of this chasing followers in the hope of a sudden viral success of whatever it is we’re all about, reminds me of something. It reminds me of the last years of the 20th century when everyone was swapping banner ads on their web rings. It’s not actual productive work. Yes, it gets the word out there and an amount of that kind of promotion is a good ingredient, but it can’t take your whole day, day after day. If everyone did that, nothing would get made, grown, produced or fixed. My advice therefore is to concentrate far more on what it is that you produce that is of value, and less so on publicising it, otherwise you’ll get nearly nothing done in life. Turn your back, get on with whatever it is you actually do and make some more of it. Be productive. You can market it afterwards. Unless, that is, your whole productive output is structured only around social media “marketing”, in which case you’re effectively useless. But that can’t be the case, I’m sure you can actually do something that people are interested in experiencing.

What is a network? Scale-free networks

Previously I mentioned Preferential Attachment (the “rich get richer” phenomenon of some networks) which explains why popular nodes in a network become highly connected, and are highly connected because they are popular, and are popular because they are highly connected, etc. We see this on the Internet as things either go viral or things basically don’t move at all, plummeting to obscurity and beyond! It happens with people, some of us are highly connected, some are effectively islands, and most have just the average amount of connections. However, we may be connected to highly connected people on social networks, such as the Fry, the GaGa, the Kutcher types. Those superstars tweet it all and get retweeted by so many followers to their followers in turn, and the cycle is thus reinforced.

However, we could be being fooled here, as the size of the connected population is huge. Our intuition is that one follower may be fairly easy to gain, two followers must be twice that much work, ten followers, ten times that time and effort. A hundred thousand followers must take more than a lifetime to achieve!

How old are you? More than likely somewhere in the range of 20s to 70s, with a few outliers outside of this range. It’s rare to encounter someone older than 100, it is predicted that the first 150 year old person has already been born. Maybe. Maybe in the distant past a person did reach 150 but nobody wrote it down. Maybe H5N1 will mutate into human to human transmissible form soon and wipe out two thirds of the worlds overpopulation. Who knows? The point is, we’re used to a certain range of ages, and to find someone over a century is unusual. We never encounter a person over a thousand years old. Or a hundred thousand years old. We never encounter a person taller than the tallest building. We never encounter a person several thousand times more intelligent than average. What about strength? What about shouting loudest? What about jumping highest?

These parameters are kind of within “human scale”. We’re used to thinking about a kind of tangible scale, expecting measurements to fall within certain familiar boundaries, and applying a linearity to these dimensions. A ten year old took ten years to get there, a thirty year old, three times that much! I dug a hole 1 metre deep in a day, in ten days it was 10 metres deep. And so on.

However, in some networks, we experience an alternative dimensionality of Scale-Free networks. These are networks in which certain dimensions might have a mean of a certain value but it’s easy to find a few instances of crazy escalation up into the sky. That’d be like walking around and seeing most people about the age of a human, but now and then meeting someone that was around in the Cretaceous era. This is a scale-invariant situation — there’s no human scale to it any more. The results might be said to follow a power law distribution or Pareto distribution. Superstars getting insane amounts of connections in social networking while the rest of us will never get beyond a few thousand (or a few, in many cases). The spread of the World Wide Web and the quantity of websites on it. The relative growth of wealth of Bill Gates, Mark Zuckerberg, Larry Page, Sergey Brin, compared to the growth in earning power of all those in the same class as those people at school.

Most people work in a job and get paid. The job requires a certain amount of work as the input, and in a fair situation, it pays somewhat under what you’re worth as a reward. Therefore we’re used to thinking about income in a way that has a linear relationship. I do a certain amount of work in a week, I get paid a certain amount of money in a week. Sounds fair? That’s how it is. So how is it we have examples of super-rich billionaires? Do they do vastly more work than you and I? I’ve only got 24 hours in a day, and so have they, so how do they get a hundred thousand times more work done than I can? It’s not fair. Why can’t we go to our boss and ask for a pay rise, of a hundred thousand times what we’re getting now? Sounds fair? Sounds fair to me.

What is a network? Direction jobs letters

Previously I discussed networks and the notion that we use the word “network” all the time. We don’t fully appreciate all that the word connotes, so that what one person thinks of when you say “network” is quite different to another person’s thought.

I mentioned Euler’s solution to a famous “seven bridges problem”, what would become graph theory, with vertexes and edges. The London Tube map is a diagram of nodes and connections. Some stations are highly connected, acting as hubs between many tube lines, some not as many interchanges, but most are connected to only their previous and next station. Bank; Waterloo; Kings Cross; Hammersmith come to mind. If you change lines on your journey, stations like those look like good interchange opportunities and become quite busy — everyone uses them at once. This usually means that more people choose to use them, demonstrating the “rich get richer” behaviour of many networks, called Preferential Attachment. Highly connected vertexes become even more popular because they are highly connected.

I mentioned Six degrees of Separation, that having a close group of people has disadvantages. A homogenous group of people all interested in the same thing for the same reasons are prone to solving the same problems the same way, making the same mistakes, and processing new information with little variance. They spread ‘interesting’ relevant news rapidly with the effect that everyone in the group soon knows what everyone else in the group knows. This might sound nice and cosy and cohesive, but wait. What if one of the group leaves their job?

Some connections between nodes, in other words, some edges between vertexes, are asymmetrical. In other words, they only go one way, and don’t go back. In effect, they are arrows that only point one way. There may be a way back, via a different edge. Or there may not.  In such cases, the network becomes a directed network. The food chain is a directed graph, wolves and rabbits are connected. A wolf often eats a rabbit but a rabbit never eats a wolf. A rabbit eats lettuce but lettuce never eats a rabbit. Think of your own personal social networks. Chances are many connections have directed behaviour too. When job hunting, it feels different asking for a reference from your boss than a friend or coworker, the result may be different too. The directed network has an effect on the shape of the network and the timing and flow of information into it and out of it (if any flows out).

It wouldn’t be a surprise to say that a lot of people got their job not because of a cold application in response to a job ad, but because they knew someone, or knew someone who knew someone. When faced with job-hunting again, people will often reach out to those in their immediate networks for any information that might help (as if they were withholding info until just now). People in our own networks know and share the same information and are interested in the same kind of thing, noticing the same kind of opportunities as each other. Widening the range of contacts to people in the network much further away in terms of degrees of connection may actually give better results.

Those distant connections are exposed to other networks that your colleagues might not be, carrying other news not available within your immediate network. Mark Granovetter wrote in 1973 on the “strength of weak ties”. You may find a certain type of person at the periphery of networks, not afraid to cross over into other departments or groups of disciplines. The type of person not willing to pigeonhole themselves and interested in many and various endeavours in life, with contacts across them all. This can be of value — the chance to import knowledge or methods from distant departments. This type of person incidentally is often a catalyst where disruptive innovation can occur, crossing techniques and methods from one discipline they’re exposed to, to another. Even within our own organisations, departments elsewhere in the same company have different and valuable knowledge. If only they were connected. This is the notion of social capital.

In 1967, Stanley Milgram carried out an experiment forwarding letters to strangers to gain more information on the “small worlds property” of some networks. Even at that recent point, debate arose over how many degrees of separation existed in typical real-world networks that we are all familiar with. Exactly how connected was our world? Would two random people in a population know each other? Directly? Through an acquaintance? Through more links than that? The experiment at Harvard was designed to find the average path length between two nodes in the network, in this case, nodes being people. Random people in chosen cities in America were sent a letter to forward to someone in particular, if they knew them, and if they didn’t know them, to send it to someone else they imagined might know the intended recipient. There’s a lot more to the experiment than that, of course, the package introduced the experiment and had postage paid replies to invite participation; tracking postcards back to Harvard, etc, but essentially that’s what the experiment did.

The results were quite interesting and somewhat revealing. In one part of the experiment, 160 letters went out and 24 hit the target, sent to his home address, but 16 of those 24 all came through the same person, a clothing merchant identified as “Mr Jacobs”. Others of the letters came to the target through his office, and over half of these came directly through two other men. Why so many coming in through so few? Are these people acting like the busy stations on the London Underground? Are those men each playing the part of a kind of social hub? This is quite possible. Some people are highly connected, and their highly connected nature increases their connectivity as people favour connecting to the already highly connected — again, Preferential Attachment (the “rich get richer” mechanism), except we’re not necessarily talking about financial riches, but richness of social capital in their social networks.