Network science, influence and the social web.

"At any moment in time, we are driven by and are an integral part of many interconnected, dynamically changing networks" - Katy Börner, Soma Sanyal and Alessandro Vespignani

NetworkMy original 3 R's of Influence proposal was compared to the principles of network science due to the nature of data and relationships required in order to ascertain a full picture of our influence over others. Network science was not something I was overly familiar with at the time so I have decided to take another look at how social networks and influence fit together based on these principles.

As a reminder, I proposed that social influence should be comprised of: reach, reputation and relevance.

We must also guard against the difference between perceived and actual influence where perceived influence is little more than garnering attention with single click, throwaway behaviour such as Likes or +1s.

Actual influence is encouraging someone to do something meaningful: a comment that adds value or writing their own post, changing their opinion or maybe even influencing a wider decision such as a purchase.

So, what is network science?

One definition of network science is "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena"; it is essentially the study of any kind of network, its formation, the behaviour of its members and the analysis thereof.

If you have spent any amount of time discussing the operation of social networks then you will already know more about the field than you might expect from the terminology involved to some of the core, common sense concepts:

  • A network (or graph) is composed of nodes (members) connected by edges (the links between them) - edges can be bilateral or unilateral and determines the type of network we are dealing with.
  • Bilateral links will create the formation of undirected graphs (or just graphs) which, from a social media perspective, we will recognise as having a "friending model" - nodes will enter a reciprocal relationship.
  • Unilateral links will promote the creation of directed graphs (or digraphs) which we will recognise as the "following model" - just because Person A follows Person B it does not imply that the connection goes both ways.

Directed and undirected graphs are often examined in isolation but, in reality, our networks comprise a mixture of bilateral and unilateral links and exist within the context of wider connections. We are frequently active on more than one social network so really need to investigate "multigraphs" as our connections often exist in more than one network and we have multiple edges between the same individuals depending on the means of connection.

We might have a bilateral edge between users on Facebook (friends) but only a unilateral edge on another service such as Twitter or Google+ (a one way following).

It is the combined impact (and not necessarily the sum) of these edges that, ultimately, determines the influence exerted by one node on another - we may not enjoy the same relationship on different networks.


Social influence measurement systems such as Klout and Kred attempt to operate in a multigraph environment but, as has been stated previously, often only have access to limited public data which cannot accurately determine the level of influence.

A data host, such as Facebook or Google, has direct access to both public and private data and also access to an extended set of "actions" so is far better placed to determine influence between nodes within the confines of its own graph but this acts in isolation and any potential ranking is independent of influence within any other graph unless the data host has sufficient access to other data sources - Google may have access to extended data via its search engine for example but certain private data will still be missing.

Random NetworkFriends and weighted graphs

As well as the number of edges (roughly translating to the number of friends) we may have, strength and frequency of interactions between nodes have an impact on the graph - and therefore the degree of influence exerted by those nodes.

Network science defines a node with a direct connection as a Neighbour - within the social web we will refer to this as a friend or follower based on the nature of the connection.

Connections between people are known as paths and if we are able to go from one node to another along a path - even if it means going via intermediate nodes - then this node is within our reach. Still all familiar terms.

Reach is perhaps an impersonal term so we tend to feel more comfortable with the likes of Facebook's "friend of a friend" but it still means exactly the same thing: someone connected via a path and, therefore, within our reach and potential influence.

The length of the path (how far removed a friend actually is) will usually determine the extend of influence but the influence afforded by specific events may override what is expected. Person A may not normally influence Person B very highly due to the social distance between them but a specific share may prompt action beyond the normal response for that path. This may be an isolated event, in which case it will have little impact on overall influence, but it may also cause Person B to create an edge (friend or follow) with Person A thus directly increasing the base level of influence between them.

As I have previously mentioned with regards to implicit and explicit graphs, the frequency of interaction can increase the degree of influence, especially for secondary/tertiary connections etc. The more frequently someone is exposed to a friend of a friend the more likely they are to be both influenced by them and to create a closer connection - just like the move from a repeated implicit graph to an explicit one.

The actions of our friends and followers (neighbours) can be seen to be very important in the determination of strength of connections and also the way our clusters are formed.

GravitySocial gravity

The concept of "graph density" is quite obvious: if the actual number of edges between nodes is close to the maximum possible number of edges then it is a dense graph. If a group of nodes within a larger graph is particularly dense it can be refered to as a cluster. A typical example is a group of friends on Facebook who all know each other.

The denser the graph the greater its influence due to increased communication between the nodes. A denser graph can be thought of as having its own "social gravity" - the more connections and interactions we experience within a group the more included we feel and, therefore, more likely to remain a member. A sparse graph is likely to have less regular interaction between members on its periphery and they are more likely to disconnect in search of a more fulfilling experience.

We can argue that influence is not only the ability to cause others to perform actions but to also maintain graph/network integrity even without necessarily prompting action; this can be the cumulative effect of the actions of members within the group rather than specific individuals.

Influence is not just for people.

Degrees and herd mentality

The number of connections (edges) that a node may have is known as its degree. The higher a nodes' degree, combined with the degree of those nodes to which it is attached, the more likely that it is "central" and, therefore, an influencer - all well and good we would assume.

The "Barabási–Albert (BA) model" for network generation states that as a network grows so those members with a high degree are more likely to receive new connections and we see this in action all the time within our social networks.

As individuals, our own social gravity will determine our ability to attract new followers but an element of herd mentality can also be at play. For every follower that connects due to a genuine interest there will be more who connect as it is the fashionable thing to do as that person is deemed an influencer.

New users of a social network will frequently seek out the popular, the influencers in an attempt to increase engagement during their first weeks or months on the service.

Social gravity can, therefore increase artificially rather than organically; the graph will experience an element of distortion especially when the network publishes a suggested user list based on the perceived popularity of its members.

It is not just the networks themselves that can cause potential issues when recommending other users. The practice of circle sharing on Google+, or list sharing on Facebook, are examples where fashion may override interest and, as I wrote in my post Do shared circles aid growth or hinder engagement? blindly adding shared circles or lists and not interacting with their members can skew the graph and also have a negative impact on influence.

The ratio of interactions to edges is important; as we have seen above, whilst having a high degree may seem like a node is influential it is the weighting of its edges that is the true mark of influence. A high number of edges all with very low weighting demonstrate that the central node does not actually exert that much influence as the strength of the connections (and consequently the ability to drive actions) is weak.

ConnectionsDegree correlation

Although it may be more prevalent for relatively unconnected users to seek out popular members we can also experience instances where nodes with a high degree (influencers) may prefer connecting with other influencers. This process is known as degree correlation and a frequent example is subject experts preferring to collaborate with other experts rather than the lay person.

The social web, however, is a great leveler allowing so degree correlation can be viewed as nothing more than social snobbery with influencers merely "broadcasting" to their followers but not interacting. This might work for some as their followers might just be willing to consume; for others, however, it can lead to a sense of resentment with the influencer seen as elitist.

Our social networks

When dealing with social networks we are almost always talking about clusters when we refer to our social graphs - small subsets of the network population. Some may only interact within a single cluster (a specific, contained group of friends) and others will have connections to many based on varied interests introducing a complexity that cannot be easily modeled.

Facebook is seemingly singular amongst social networks in that its functionality is obviously highly derived from network theory. Edgerank is a direction interpretation of the effects of edge weighting to determine influence between nodes. What annoys some users, however, is the impression that Edgerank assumes that users are ONLY interested in what influences them most and that, over time, this ranking becomes artificial as they have filtered items forced upon them and smart lists auto-populated with those deemed close friends or just acquaintances.

Twitter is all or nothing; we see everything from someone or nothing (unless it is shared by a mutual connection). At its core Google+ is all or nothing - we add someone to a circle or we don't - we do, however, have the ability to manually weight those circles thus increasing or reducing their visibility within our primary stream. By tuning our circles we are specifying who we are (or want to be) influenced by. We are manually adopting the principles of network science without knowing it by altering the edge weighting ourselves rather than having it automated.

Both Facebook and Google+ provide the means to circumvent edge weighting by showing "Most Recent Stories" or viewing individual circles respectively but this relies on the user; many will not toggle the view of their Facebook feed or view individual circles.

What of the 3 R's?

Network science adequately covers the concept of reach as we seen above and begins to touch on the idea of reputation when we start addressing social gravity and the weight of our connections.

While a number of models exist for the formation and growth of networks the one thing they cannot accurately represent is relevance. The human factor involved in our interactions is unique and, as has been written before, what is relevant will change based on context including:

  • trust
  • interest
  • location
  • platform

The level of trust placed in an individual might be indicated by the number, strength and duration of connections but all too often we will let our social circles stagnate and not remove those with whom we no longer interact.

Our interests will vary according to our circumstances so the workings of any social group will be hard to predict once we factor in variables such as location and platform - be it mobile or desktop, different operating system or applications or different social networks.

Influence scoring

All this aside, we recognise base elements of the organisation and behaviour of our the social web in the principles of network science and this can serve as some degree of comfort to our time spent online - a validation that there is, perhaps, more to it than just meaningless status updates. We can also see these principles at work in the methods employed by the influence measurement systems as they seek to evaluate the impact of our connections across the range of social graphs.

Opinion on the efficacy of influence measurement services is widely contradictory. The science behind the likes of Klout and Kred, however, is actually quite sound but calculations based on a flawed data set are always going to be problematic.

Social influence measurement in its current form must not be used in isolation but can be treated as a base on which to add the more human elements of online interaction.

Images by futureshape, OpenBioMedicalRubin 110 and bupowski

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Colin Walker Colin Walker colin@colinwalker.blog