Sunday, March 23, 2008

What is Your Network Diversity Index?

In a previous blog post, I likened my network to a biological community. This was in an effort to provide a means of analysis of what was becoming the source of information in my personal learning environment. For the sake of the discussion I will classify individual (node) of my network as a member of a species. Also, in the case of my network, a species is an organizational construct rather than a genetic one. (See taxonomy in Wiki here).

The structure of a biological communities is very much a function of spatial and temporal interactions. For example, analysis of a non-tropical, climax community would show that it is comprised of very few species (low species diversity). In contrast, an equatorial tropical rainforest with moderate climatic conditions, high photoperiodism and few limits to colonization, show a relatively higher degree of species diversity. Climax communities, then, have a major fraction of the flow of energy/biomass involving very few species where in rainforests, that energy/biomass is not isolated but dispersed.

A learning network with a structure similar to a climax community would have a great deal of its information emanating from individuals of a very similar background thus creating the "echo chamber" effect. Whereby our associations with similar minded individuals creates a conversation whose point of view may be echoed by those around us limiting the opportunity of new/different ideas. The measure of species richness in a biological community (and information richness in our network) may be assessed by creating a diversity index.

The relationship between of the number of species in the community to the number of individuals in the community is shown by a ratio known as a diversity index:

Where D= Diversity Index
A = Number of species
B = Number of Individuals

The problem here is when the number of individuals is much larger than the number of species the diversity index will be very small. This could be corrected somewhat with the following:

Still, very little information about community structure is derived because as long as you have say, 5 species and 100 individuals, your Diverstiy Index will be .50 no matter how the individuals are distributed across the 5 species.

There have been many attempts at refining this index but the one I remember from an undergraduate Ecology class was called the Shannon-Weaver Index (revisionists now call it the Shannon Index).

Where: d = Index of Diversity
s = Total number of species collected
ni= Number of individuals in th ith species
n = total number of individuals


simplifying still:
The Shannon function combines both the number of species and the the uniformity with which the individuals are distributed among the species present. The presence of both an increasing number of species or more equitable distribution of individuals among those species will result in an increase in species diversity.

For example, consider three networks each consisting of 100 nodes (individuals). Those 100 individuals are representative of 5 different organizational groups (species). Here is the interspecies distribution for the networks:

You can see here that all networks have a total of 5 groups and 100 individuals. Network A (top) exhibits the most equitable distribution of the individuals while community C (bottom) shows the least equitable. While all networks will have the same species diversity index of 0.50 (see earlier calculation), network A has the higher Shannon index.

This may allow an individual to analyze his or her network as it develops over time.

If, like myself, the math makes you wail and gnash your teeth, try the following. Evaluate your network, divide it into groups, give each group a number and determine how many people you have representing each group. Then follow this link to a Shannon Index calculator, enter your the number of people you have in each group, compute and read the value for H1.

I'm not sure of the value of this index on small networks. In ecological studies a random sample of the community is done with a sample size of 100. Also, while this does evaluate diversity and equitable distribution, it doesn't evaluate something like "trust" as mentioned here in a presentation by George Siemens in Dr Alec Couros' EC&I 831 course.

I am indebted to my notes from my ecology class at the University of West Florida under Dr. Gerald Moshiri. I am also indebted to Roger's Online Equation Editor for generating the equation images in png format.

Thursday, March 13, 2008

Network as Biological Community

Recently, Alec Couros, in preparation for a presentation to his faculty, tweeted the question,"What does your network mean to you?". As a tribute to the vitality of his network, the responses (twice) produced a host of comments (collected in a Voicethread here) to answer the question.

As a self-proclaimed digital primitive, I began to answer the question with analogs to the Ecosystem component of the Biology content I teach. If the internet has become the landscape of our Personal Learning Environment (PLE), then I will employ a Synectics strategy I use with my students and create the metaphor; "Networks as biological communities."

We might define a biological community as all the interacting species within a habitat (or biotope). My learning network is a community of interacting individuals within my learning environment. Now here, I first rushed to consider that each individual member of my network would represent a different species. After a bit of mental wrangling, I realized that was incorrect. I should consider each person in my network as a member of a population which is "a group of individuals of the same species". What defines a species in this analogy and the identification of which species inhabit our "environment" will take some work. (I'm thinking a wiki may aid in this discussion).

Alec utilized the diagram above, which he had developed some time ago, as the visual for the Voicethread. Entities at the perimeter of the diagram (Web 2.0 "tools" if you pardon the expression) are ways in which other individuals in our networks perceive us and interact with us. They represent codes for who we are, thus, in the analogy, our DNA. As is true for our DNA, these codecs are able to be replicated, mutable and adaptive and in light of changes in the environment, some become more favorable than others. For example, where a web page once was the dominant form of expressing oneself, in a 2.0 environment, blogs and wikis are more favorable. Thus, blogs and wiki are selected for fitness in this environment and increase in frequency while web pages are selected against and so their frequency decreases.

This also bring in to question the definition of an interaction. What must occur in order to qualify as an interaction? Is the reading of a Tweet considered an interaction or would you have to respond to the tweet in order to qualify? Consider this, while I was unable to respond to the Voicethread directly with a comment, this blogpost was generated in response to the tweet. Some time will have to spent on categorizing the type of interactions within the network.

Why take so much time to develop the analogy this far? One, to answer the original question for myself. Two, I believe if I can fine tune the components of the analogy, there may be some ecological algorithms to develop metrics for assessing our Networks and Personal Learning Environments.