What is a “Graph” and are “Social Graphs” the only type of graph that matter?

Preface: the Web is a global phenomenon like we have never known, and one of the most amazing things about the Web is that we are all learning about it together – bound together on a gigantic global learning curve, we are starting to realise what the Web actually means together.  The below is an attempt to summarise the first lesson we have learned as a global hive mind in what I am calling the “World Wide Web Class: 101”.  As preempted by the marketing term “Web 2.0”, I also believe we have begun another global learning process that has us all learning the meaning of “graphs”, or rather what I am calling the “World Wide Web Class: 201”.  I’m hoping this post is the first in a series of posts that helps draw out the importance in the way we are globally learning about the Web and what we can expect next as we move through this global learning process together that is the “World Wide Web course” – “classes 101, 201, 301, 401… and beyond”.  The following is the start, from course www101 into www201…

What is a ‘graph’?

First off, I thought I’d attempt a layman’s description for “a graph” as contextualised by the contemporary use of it as a “social graph”: definition: “a ‘graph’ (like a piece of graph paper) is made up of lines and the places where those lines cross (we’ll call these line vertices’s ‘nodes’);

However, unlike the uniformity of graph paper a graph occurring in the real world is not evenly distributed and some of the nodes are more significant based on the number of lines that intersect.

Graphs in the real world look like spider webs, and like spider webs, graphs must have more connections to single nodes than other nodes to assure they are stronger based on the environment in which they exist.

It is also worth mentioning that graphs (like spider webs) continually change to adapt to the ever changing environment.  The most significant graph -that is commonly known- is the Internet (aka the Web), and for the first decade of the Web it was HTTP “pages” that were the most significant ‘nodes’ in the graph.  Our “World Wide Web 101” understanding of this global phenomenon was mostly understood as a graph that consisted of nodes that appeared to be ‘pages’, like the kind in a book or the essays you might write down in a paper notebook.

However as the Web has changed to adapt to its environment, we have started to realise that it is the lines between the *human nodes* that are often the strongest and most important to create, this is the ‘social graph’ and is controlled by many so-called “Web 2.0” companies like Twitter, Facebook, LinkedIn, etc.

The Social Graph Anti-Pattern (what is NOT a ‘social graph’)

Hierarchies are perhaps the best non-graph example as they are usually controlled by a single person or group, whereas a graph like facebook is dependent upon many factors in how it is created, formed and reformed (though don’t be fooled into thinking that graphs are not sometimes capable of becoming hierarchies – it is usually just more difficult to make a graph a hierarchy because it is distributed) .

The factors for how the nodes relate to one another in a graph can be described as ‘edges’.  Edges are how the nodes in a graph relate to one another.  A hierarchy -as opposed to a graph- usually has a very clear pattern for how the edges between the two nodes are created.  For example your boss as a ‘node’ has a line pointing to you (as a node) and the ‘edge’ of the node is pointing to the next person below you in the hierarchy.  The pattern of these edges moving in the same direction is what creates a hierarchy (getting the edges to move all the same way in a graph is very difficult).  Hierarchies are dependent upon ‘edges’ going in one direction, whereas a ‘graph’ has no clear direction for which way the ‘edges’ are pointing between nodes.  For example, in Twitter anyone can point their nodes’ edge at another person’s node by “following” them.  This edge is a single direction (“a unidirectional edge”) in that it is just pointing from you to them (i.e. you are receiving their information they “tweet” but they do not receive the information you “tweet”, unless they “follow” your twitter node).

Facebook on the other hand requires a two way link (bidirectional edges) where your node’s edge points to them and their node’s edge points to you.  When both nodes are pointing at each other’s edges then Facebook calls this “friends” (though I think most of us would agree this is just an “acquaintance” in human parlance).

Social Graphs are just the first of many graphs…

As you might have picked up in my laymen’s description of ‘the graph’ above, what I am trying to do is give you some mathematical terms (i.e. nodes, edges, unidirectional, bidirectional, etc).  These terms are explicitly related to a type of mathematics called ‘Set theory’.  Without having to go into the maths, their is a significant point to make in that there are predictions that Mathematical Set Theory has suggested for the evolution of graphs; in the same way that Einstein was able to predict how Relativity Theory would work from his maths, so can we know how the Web is going to progress via the mathematics of Set Theory.

To predict the future we must first realise that the Internet was the first time that the world realised the power of a big “set of things” aka a “graph”, and now we are starting to realise the importance of other kinds of graphs (aka ‘sets’);  in this case the ‘set’ of things known as ‘the social graph’ or ‘the social network’ is starting to emerge and be understood on a global scale.  In essence by using the Web we have all been enrolled in a course call “World Wide Web class 101”.  So while many marketing experts are calling this new kind of ‘social graph’ the Web 2.0 phenomenon, in actuality we are just beginning to all learn about the power of ‘sets’ or what many are calling ‘graphs’.

So while we may be in the Web 2.0 phenomenon, in actuality it is more like we have all just graduated from “World Wide Web Class 101”, in that we are starting to understand that the Web is a ‘set of things’,

And now as we enter our next course in the “WWW Class 201”, we are starting to learn that there are sets within the graph that can be linked together, with the dominant example being the social graph.


What we have yet to understand as a global populace is that there are still many new types of graphs to follow, just like the ‘social graph’ is a subset of the ‘internet graph’, now we will begin to realise that the social graph (while very significant) is a graph that can be combined with other graphs to form new graphs (let alone the subset of graphs that exist within the social graph, e.g. your business social graph, your old schoolmates graph, your future people you want to meet social graph, etc).  It is here in the complexity of graph combination and subset of graphs that the maths becomes interesting.  But more on this later…


~ by dfflanders on May 7, 2011.

5 Responses to “What is a “Graph” and are “Social Graphs” the only type of graph that matter?”

  1. A good podcast that demonstrates my point above with Mark Zuckerberg continually talking about the ‘social graph’ and what it means to facebook as it evolves:


  2. Are you sure about the whole Graph / Set thing?

  3. His is really fascinating! Brilliant discussion that really makes you consider the times we’re in… Thanks for posting!

  4. […] 1 What is a “Graph” and are “Social Graphs” the only type of graph that matter? May 2011 […]

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