Sunday, January 30, 2011

Networks, Neighbourhoods and Communities: A Reflection

1. Network Components

In Friday's CCK11 Elluminate session I highlighted some of the properties of networks in the following diagram:

Now this isn't the most official diagram in the world, but it suffices to highlight some of the properties of networks we want to include in our discussions. First, there are the two major parts of a network:

- the nodes (also known as vertices, entities, units, etc)
- the links (also known as edges, connections, etc)

Within these collections there are various properties that parts of a network may possess.

The node, for example, may have the following properties:

- the activation state - that is, the current state of the node, which may be off or on, 1 or 0, excited or at rest, etc. The activation state may be very simple, or may be a combination of a large number of factors, depending on the complexity of individual nodes.

- the number of connections (indicated by C in the diagram), or the list of the set of connections for a given node, etc.

- the activation function, that is, a description of what sort of combination or type of inputs is required in order to switch the node for (say) 'inactive' to 'active'. Activation functions may be expressed in terms of signal strength, the type of signal, or the number of signals being received. It may be an absolute value, a probability function, or some other type of function.

The link, meanwhile, may also have various properties:

- the directionality of the link, whether it is unidirectional from one node to another, or whether it is bidirectional (Twitter follows, for example, are unidirectional, while Facebook friends are bidirectional).

- the strength of the link, or the breadth of the link, which may be (for example) an indication of what proportion of a signal being sent will be received by the receiver. In formal networks, strength is clearly enumerated, but in less formal networks, we may use less formal terms ("he's a strong friend",  "the strength of weak ties", etc.)

- the type of connection, for example, 'friend', 'neighbour, etc. or nature of the interaction

- the number of strands in the link, which may be seen as a combination of different types of links, of different intensities

2. Communities as Networks

From this perspective, we now turn to the analysis of communities as networks, and in particular, I'll turn to Barry Wellman and Barry Leighton's "Networks, Neighborhoods and Communities, from Urban Affairs Quarterly, 14 March, 1979 (thanks, George, for the suggestion).

What Wellman and Leighton are trying to show in this paper is that traditional network discourse would be more effective were it expressed in terms of networks. They cite a variety of literature that examines the nature of communities in urban settings, noting that these analyses have their own frames and vocabularies to describe these communities. And they ideantify three major types of arguments in the literature:

- the 'community lost' argument - this is the argument that increasing urbanization has weakened communities. "Lost scholars have seen modern urbanites as alienated isolates who bear the brunt of transformed society on their own."

- the 'community saved' argument - communities form regardless of the circumstances. Humans are fundamentally gregarious and "Densely knit, tightly bound communities are valued as structures particularly suited to the tenacious conservation of its internal resources, the maintenance of local autonomy and the social control of members.

- the 'community liberated' argument - "people are seen as having a propensity to form primary ties... out of utilitarian ends." These ties may not be local or geographically based, but tight-knit communities nonetheless exist.

Now consider how Wellman and Leighton cast each of these three theories in network terms:

Community Lost
(a) Rather than being a full member of a solidary community, urbanites are now limited members (in terms of amount, intensity and commitment of interaction) of several social networks.
(b) Primary ties are narrowly defined; there are fewer strands in the relationship.
(c) The narrowly defined ties tend to be weak in intensity.
(d) Ties tend to be fragmented into isolated two-person relationships rather than being parts of extensive networks.
(e) Those networks that do exist tend to be sparsely knit (a low proportion of all potential links between members actually exists) rtaher than being densely knit (a high proportion of potential links exists).
(f) The networks are loosely bounded; there are few discrete clusters or primary groups.
(g) Sparse density, loose boundaries and narrowly defined ties provide little structural basis for solidary activities or sentiments.
(h) The narrowly defined ties dispersed among a number of networks create difficulties in mobilizing assistance from network members.

Community Saved
(a) Urbanites tend to be heavily involved members of a single neighborhood community, although this may combine with membership in other social networks.
(b) There are multiple strands of relationships between members of these neighborhood communities.
(c) While network ties vary in intensity, many of them are strong.
(d) Neighborhood ties tend to be organized into extensive networks.
(e) Networks tend to be densely knit.
(f) Neighborhood networks are tightly bounded, with few external linkages. Ties tend to loop back into the same cluster of network members.
(g) High density, tight boundaries, and multistranded ties provide a structural basis for a good deal of solidary activities and sentiments.
(h) The multistranded strong ties clustered in densely knit networks facilitate the mobilization of assistance for dealing with routine and emergency matters.

Community Liberated
(a) Urbanites now tend to be limited members of several social networks, possibly including one located in their neighborhood.
(b) There is variation in the breadth of the strands of relationships between network members; there are multistranded ties with some, single-stranded ties with many others, and relationships of intermediate breadth with the rest.
(c) The ties range in intensity; some of them are strong, while others are weak but nonetheless useful.
(d) An individual's ties tend to be organized into a series of networks with few connections between them.
(e) Networks tend to be sparsely knit although certain portions of the networks, such as those based on kinship, may be more densely knit.
(f) The networks are loosely bounded, ramifying structures, branching out extensively to form linkages to additional people and resources.
(g) Sparse density, loose boundaries, and narrowly defined ties provide little structural basis for solidary activities and sentiments in the overall networks of urbanites, although some solidary clusters are often present.
(h) Some network ties can be mobilized for general purpose or specific assistance in dealing with routine or emergency matters. The likelihood of mobilization depends more on the quality of the two-person tie than on the nature of the larger network.

Now what is important here is not whether one or another of these descriptions is true or accurate - this is a matter of empirical investigation. Rather, what is significant is that through the use of network terminology, we can precisely formulate these theories into a set of contrasting alternatives, the dimensions of which may be easily viewed and understood.

Note how each of these three descriptions is composed by stepping through a series of network properties: (a) membership in networks, (b) the number of strands in the links, (c) the strength of the links, (d) the number of connections an individual has, (e) the number of connections members in the networks have in general (ie., network density), (f) the coherence of the network, (g) individual activation function, and (h) network activation function.

3. Reflections

So much discussion in the field of education is based in loosely defined terminology and concepts. Take, for example, the advice to 'form community'. There are many things this advice could be manifest as, including any of the three accounts of community given above, and a wide variety of other permutations.

Typically, the advice to 'form community' is understood as advice to form solidary activities and sentiments - what I would in other works characterize as groups - but which here may be more precisely understood as actions undertaken in unison ('collaboration') and sentiments held in unison ('commonality'). But of course such exhortations are only one way communities can organize, and not even the most effective ways. But there is always no shortage of people - Larry Sanger, Jaron Lanier, Sherry Turkle, to mention a few raised recently - ready to lament the 'lost community' or 'techno-groupthink' in technology-based education.

What do these criticisms mean? What is their validity? Rather than use prejudicial and imprecise vocabulary, we can examine what it is about technology-supported learning and its proponents that bothers these authors. Perhaps it's all about a sentiment of community lost, as defined above. In such a case, we can respond to it meaningfully, with clarity and precision.

Or take the discussion of 'interaction' in online learning. While more interaction is typically lauded as better, we tend to be sharply limited to narrowly defined notions of interaction - perhaps Moore's formulation of learner-content, learner-instructor or learner-learner interaction. Or maybe Anderson's more sophisticated formulation of the same idea.

But if we can approach the concept of 'interaction' from the network perspective, allowing for the existence of many types or strands of interaction, many degrees or strengths of interaction, various interactive media, and more (as I tried to explain in this series). Again, the point is that we can use network terminology to explain much more clearly complex phenomena such as instruction, communities and interaction.

Wellman and Leighton's paper was written in 1979. It is well-worth anyone's while to look at more recent work to appreciate the depth and utility of network analysis.


  1. speaking of cross-silo connecting, I just sent the Wellman/Leighton paper to a friend working in small business and community development

  2. Stephen,

    Nice posting though I become more confused with the concepts behind networks by the day. Which, I suppose, is a good place to start.

    On Sunday night while watching an Al-Jazeera video of demonstrators in Cairo pushing the police back into their barracks the commentator noted that closing the net and cell service seemed to have little effect in dampening the protests. The speculation was that without word from your friends to rely on for updates and locations of hot spots, protesters simply had to venture out on their own. As if news from friends actually dampened the urgency to "be there" by making it KNOWN and oddly less interesting. Or conversely increasing the anxiety level by creating a vacuum of information that could only be resolved by personal attendance.

    I'm trying to understand if this is a dynamic of networks? To actually rush to the scene of silence, as if no-news was a more powerful attractor than full coverage. Of course, those used to an abundance of network activity may tag silence as a most extraordinary event which compels resolution by whatever means is available.

    At first I was thinking this had something to do with the influence of weak interactions--as in the network conversation is weakened by being turned off. But it feels more like the power of a network to remain intact by adapting to changing conditions. Is it a characteristic of a network to seek equilibrium? If so, there must be some sort of shared identity that allows many individuals to collect and disburse. Can that be simple group membership? Or something different?

    Scott Johnson

  3. A more recent study, and arguably a more relevant one, is the RSA report, "Connected Communities." The whole report is found here:
    It develops language such as social resources, social capital, and social networking analysis. Building on the information provided in the RSA's Social Brain Report, "For the last two decades, the model of the rational individual- 'homo economicus'- that has underpinned our faith in democracy, reliance on the market, and trust in social institutions has been consistently undermined by social psychology, behavioural economics and neuroscience."

    Sherry Turkle, who in her 1995 book "Life on the Screen" had high hopes for the positive aspects of the digital age, raises interesting concerns about the effects social media can have on social networks in her in book, "Alone Together". "We aren’t “happy” anymore: we’re simply a semicolon followed by a parenthesis." she laments. And this can apply to the on-line learning community as well, where discourse too often is reduced to words on a screen. But we need to be reminded that social media and the communities it forms, such as Facebook, are the same point computers were in the 1980's, in term of the evolutionary experience that may be afforded us in terms of moving beyond geographic community.

  4. In Network Components, there is a major omission. Learning rule.

    If you use diagrams directly or indirectly borrowed from associationist or connectionist models to give some credence to your ideas, you might as well provide to your audience with the knowledge they need to evaluate the value of your propositions.

    Neural networks are absolutely useless unless they are trained. Knowledge is acquired via some mechanism. Common ones are hebbian learning ( or retro-propagation of errors (

    Worth a read too: "Letting structure emerge: connectionist and dynamical systems approaches to cognition"

  5. > If you use diagrams directly or indirectly borrowed from associationist or connectionist models to give some credence to your ideas

    @Anonymous: Don't be snide unless you've done your research. I've been working and writing on these ideas for decades. I am very familiar with associationist and connectionist principles and people who are familiar with my work know this.

    I appreciate the references to some discussions of associationist learning principles, which I've discussed in many talks over the years. The three I refer to most frequently are Hebbian associationism, back propagation (as it is properly called) and Boltzmann mechanisms.

    Obviously, not everything about connectionist and associationist principles can be covered in a single post. This post is introductory, intended to familiarize readers with basic components of networks, and no more.

  6. @Downes I am surprised that you never heard the term "retro-propagation" as it has been used interchangeably with "back-propagation". cf "the retro-propagation algorithm, or back-propagation algorithm." I used the more generic retro-propagation as the term back-propagation is strongly associated with the PDP model of Rumelhart and McClelland (1986) which assumes a layer of hidden units between input and output, an idea that is difficult to apply to the notion of nodes between people. To be successful, the back-propagation algorithm also must assume non-linear activation functions which are difficult to transfer to human networks as well. Neither hidden units or non-linear activation functions appeared in your diagram or explanations.

  7. Anyway, you haven't addressed the main point. Heavily interconnected networks that you used in this article as analogy for human networks are useless without a learning algorithm.

    You say "Connectivism is a learning theory" but later, you claim "Hence, in connectivism, there is no real concept of transferring knowledge, making knowledge, or building knowledge". So, do you have a learning theory or do you have a theory that explains that no learning should ever be expected to take place when people randomly connect, in non structured way over the internet.

    That it could be the later rather than the former is much substantiated by the content of that page "What is connectivism". As you state, you have been working and writing on these ideas for decades. You also have worked in the field of instructional design for at least as long.

    You have done so, mostly, using the connected approach that your promote. You use your own success as an illustration of the value of that approach. But what is the value? The connectedness that you practice yourself is mostly in a kind of guru mode. One-to-very many without any rigorous feedback mechanism obviously. Comments on the blogs suggest that over time, the audience has limited itself to converts. Is this kind of connectedness a good thing?

    Which brings me back again to my main point. The absence of any learning rule, of any retro-propagation mechanism in your model of human connectedness. The absence of any mechanism to warn you and provide critical information when the reality is not quite what you assume of it. What are the possible dangers to not introduce in the system any mechanism that will help keep in check the need we all have for feeling important (status and identity).

  8. Red: If this is what connectivism is, then it has negative value to education.

  9. Tracing a group of people in a virtual course without any programming software, How we can trace the nodes in a simple virtual course? Maybe using sociogram, drawing the positions or exist any friedly Web 2.0 tool? My thesis project is a virtual course for tracing the connections and networks so..I know spicynodes any other tool? Grasshopper is complicate for me....

  10. Anonymous, the Sandu and Leon paper does not support your point about the use of the term 'retro-propagation'. The term 'retro' is used exactly once, and not in any of the references; 'back-propagation' is used 10 times, in some section headings, and in various references. The term 'retro' is described in the paper as equivalent to the much more widely used term 'back-propagation'.

    As for, "do you have a theory that explains that no learning should ever be expected to take place when people randomly connect," you may want to look at this paper which uses the concept of induction as an analogy to explain how a non-transfer theory works.

    Finally, while I welcome comments critical of the theory or any of the work I do, I do not welcome the snide and sometimes rude tone of the remarks. Personal attacks (ie., any sentence that describes me, rather than the issue) are not acceptable. Comments that are not professionally written will be deleted from this thread without notice or comment. Last warning.

  11. "The learning algorithm referred to as backpropagation (or more formally, retropropagation of error) " -

    The point I am trying to introduce really is not about the specifics of the backprop nets. It is about the notion of "retro-propagation of error" and the fact that in the absence of any mechanism of this type, highly connected networks are known to be useless.

    That was left out of the graph. It is as well left out of the connectivist theory. Without such mechanism, no new knowledge emerge. Or as you are not keen on the notion of knowledge construction anyway, the best way to phrase it in connectivist terms is that this leads a lot of noise propagating through the connections, with no outcome, no improvement in the network performance, no "growth".

    The guys at CMU have had 30 years to think about connectionist theories given that some of the most important teachers in that field work there. McClelland, O'Reilly. That university is famous for active cross-disciplinary collaboration.

    Yet, when it came to implement their own openLearning Framework,, they put a lot of importance on the feedback mechanism.

  12. (part 1)

    The main point I want to make here is that it is simply not true that I have not addressed the topic of backpropagation, and that it is not true that it plays no role in connectivist pedagogy.

    I talk about network learning routinely, as it is a core element of the theory. It is quite right to point out that the concept is not mentioned in the post above. But it is not correct to say it is not addressed anywhere in my work.

    Here, for example, it is briefly mentioned: Slide 33, where it is used to underlie the actual descriptive principle of pedagogy (because, you know, teachers in classrooms can't 'back-propagate' - rather, corrective mechanisms are described in terms of 'reflection', 'interaction' and 'feedback'.

    I also talk about them in a little more detail here:

    Let me quote at some length:

    <<< there are other principles of association. I would like to list four (usually I list three, but I think that the fourth should become part of this picture). I'll give brief examples of each:

    1. Hebbian associationism. People are connected by common interests. Affinity groups, religions, communities of practice - these are all examples of similarity-based association.

    2. Accidental, or proximity-based, associationism. People who are proximate (have fewer hops between them) are connected. You may have nothing to do with your neighbour, but you're connected. The mind associates cause and effect because one follows the other (Hume). Retinal cells that are beside each other become associated through common connections.

    3. Back-propagation. Existing structures of association are modified through feedback. Complain about the 'me too' posts, for example, and they decline in number. Adversity creates connections.

    4. Boltzmann Associationism. Connections are created which reflect the most naturally stable configuration. The way ripples in a pond smooth out. This is how opposites can attract - they are most comfortable with each other. Or, people making alliances of convenience.

    Two of these forms are qualitative. They are based on direct experience. They are not critical or evaluative. They tend to lead to groups.

    The other two - Back Propagation and Boltzmann associationism - are reflective. They are created through a process of interaction, and not simply through experience. They are critical or evaluative. They tend to lead to networks. >>>

    Now, there are several criticisms that are accurate and useful:

    1. I do not have a comprehensive set of references for each of these four forms of network learning. Typically I just refer back to Rumelhart and McClelland, but clearly more detailed and recent work is needed.

    2. I do not describe these in sufficient depth, with a cashing out of the very general principles of back-propagation. This is work that is high on my list of priorities. My next Huffington Post article is intended to address association and connection-formation specifically. If you look at the dates you'll notice my series has stalled. I'm working on it.

    3. There is no clear back-propagation mechansism in connective courses. This to me is the most interesting of the observations and one well worth exploring in some detail.

  13. (part 2)

    Some history: the theory of connectivism wasn't intended to included courses at all. Certainly that is not my preferred approach. The idea of the course - an event limited in time and participation - is almost the opposite of networks.

    That said, the value of the course seems to be the creation of new connections between participants anew. It is as though each new course shakes up the network and allows it to grow again. Now that's not back-propagation. But it does address some of the problems of purely associative network formation.

    The comments and criticisms people who are in courses receive could (broadly be speaking) be thought of as back-propagation on an individual level. But this would need to be looked at in more detail. Do connections actually strengthen and weaken as a result of criticism? I can't imagine that they don't - but there's no way I would support such a simple inference as "person A criticizes -> x connections are impacted". I know it's not remotely that simple.

    Similarly, what about connections between people in a social network. Are there things that strengthen and weaken connections between people; it there a feedback mechanism to group-formation that tends to dissipate the group, or parts of the group. Arguably. Would I expect a nice neat statement of 'event A -> weakening of group B'? That is probably too much to hope for.

    All of these are empirical questions. They can't even be decided simply by looking at courses or groups or people learning. They have to be modeled, and the scenarios run over and over. I am very aware of this. I have always taken care to underline that the things I have to say on learning mechanisms must always be subject to actual empirical investigation by people who specialize in these fields.

    But, of course, it is not possible to run through the full set of qualifications in every single blog post. That's why it's important to consider my work as a whole.

    The references added to this post have been useful and appreciated. More references (especially to open access material that I can accually read) would greatly assist my work on the post on learning mechanisms I am currently writing.


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