Social Capital Within Social Health Networks

Welcome to Full Metal Health. Here you can follow the technical goings on of PokitDok via the blogosphere. Like you, we take health decisions very seriously and because of that we take creating the technology that drives those decisions very seriously. Here we'll be discussing all things related to the technical considerations of building large-scale, socially focused, personalized health-related technologies.  This will include novel solutions as well as epic failures we've encountered (because if you're not breaking software you're not coding hard enough!).

We'll also be sharing our observations and general pearls of wisdom with regards to the world of cutting edge software.  We'll be discussing such topics as web architectures, distributed processing, types of data stores (both persistent and in memory), machine learning, data mining, graph theory, and arbitrage environments just to name a few.

Fundamentally our journey together will be focus on how to create the technology and observable metrics of a personalized social health network with real price transparency for you, the consumer.  We've witnessed a substantial new movement in network research, with the focus shifting away from the analysis of single small graphs and the properties of individual vertices or edges within such graphs, to consideration of large-scale statistical properties of graphs. This new approach has been largely driven by the proliferation of social networks and it's not uncommon now to see networks with millions or even billions of vertices.

Let's jump right in:

I'm going to discuss a fundamental tenet of the socially focused, consumer driven health site:  triadic closure within a network

Many of you are probably familiar with the essentials of graph theory. That said, I want to focus on an important concept in the field called triadic closure.  Triadic closure basically says:   

If two people have an acquaintance in common, then there is an increased likelihood that they will become acquaintances at some point in the future.

We can depict this in a graphical representation of said tenet:

Edge between B & C is triadic closure because they have a common neighbor, A

If a node satisfies strong triadic closure, and is involved in at least two strong ties, then any local bridge it is involved in must be a weak tie.

If nodes B and C have acquaintance A in common, then an edge forms between B and C, and will produce a commonality between all nodes via a triangle network.  The term triadic closure derives from the B-C nodes closing the triangle.  Significant scale connections within a social network occur due to this closure construct, which then connects larger networks.  The basic role of triadic closure is to ascertain the probability of these strong tie closures occurring and when they will occur.  Computing these affinities is currently the focus in large-scale networks, which in turn, allow such representations as the ability to rate content, followers, and friends.

One can determine the probability of this closure by the clustering coefficients of the nodes with respect to the closure.  A definition of the clustering coefficient is usually given by Watts and Strogatz: "Collective dynamics of `small-world' networks", Nature (1998)", who proposed defining a local value, which is usually used in social contexts.  The following equation is generalized for the whole network is given by as the average of the local clustering coefficients of all the vertices:

Clustering Coefficient (Watts & Strogatz)

There are however other definitions of clustering coefficients used for societal networks so one must take care when using or referencing these computations. In general, regardless of which definition of the clustering coefficient is used, the values tend to be considerably higher than for a random graph with a similar number of vertices and edges.

Returning to the importance of triadic closure for many types of networks the probability that the closure occurs is also based on the opportunity for the friends within a network to meet.  A second reason for computing the probabilities of closure within a network to occur, in addition for a friendship to occur, is that the formation of a friendship and what occurs within that relationship of strong ties.  The strong ties of a relationship give the connection of the two nodes of the network a trust factor.  Which then converts to incentive. These attributes are the basis for formation of social capital, which drives human capital.  It's this symbiotic relationship that we will continue to explore within the context of Full Metal Health.

Until next time,

Share the health. It's time.

Ted Tanner Jr (@tctjr)

About Ted Tanner

Ted Tanner, Jr. is the Co-Founder and CTO of PokitDok. Ted has had architect positions at both Apple and Microsoft and has held instrumental roles in several startups, including digidesign (IPO and acquired by Avid), Crystal River Engineering (acquired by Creative Labs), VP of R&D at MongoMusic (acquired by Microsoft) and Co-founder and CTO of BeliefNetworks (acquired by Benefitfocus). He was also the CTO of Spatializer Audio Labs (NASDAQ: SPAZ), a company specializing in digital signal processing solutions.

Ted is on the Clemson University Restoration Institute's Executive Advisory Board, the Industry Advisory Board (IAB) for the University of South Carolina Computer Science Department, the IAB for the Center for Intelligent Systems and Machine Learning at the University of Tennessee, and Advisor to the College of Charleston's Department of Mathematics. He has published numerous articles in leading technical magazines and holds several patents in the areas of blockchain, semantics, machine learning, signal processing and signal protection.

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