Social Network Theory

Social Network Theory

In the last few decades, interest in Social Networks has seen explosive growth with Facebook being the poster child. Indeed work had gone on before that time in Physics especially in the area of “random networks” (Erdos and Renyi are famous names). In such networks, each new node is randomly connected to any previous node and its evolution studied.

The work of Barabasi and others showed that while the physics of Random Networks was interesting, it had little to do with “human made” networks such as Web, Internet, friendship networks, etc. They all fall into the category of “Scale-Free Networks”.

Scale-Free Network (SFN) Model:

“Scale-free” refers to the nature of some networks where its diameter (average # of links to reach a node from the present node; remember “six degrees of separation” between people) is mostly unchanged as the network grows in size.

SFN’s degree (# of links per node) is distributed as a power law (and not a binomial distribution which is the case for a purely random network). A well-known example of power law is Pareto distribution (“80/20 rule”). SFNs arise in networks that grow and have preferential attachment property while growing (exhibits “rich get richer” and “first mover advantage” phenomena).

Figure 1: Pareto distribution (example of a Power Law distribution)

If a “fitness” rating is attached to each node, a new phenomenon of “winner takes all” emerges (Google search engine will rate very high among websites as an example). This has been shown to be a “Bose-Einstein” condensate state (somewhat similar to condensation transitions that occur in traffic jams where long queues of cars are found, in wealth distribution models where a few people might have a hugefraction of all the wealth and in operating systems usage where Windows has close to 90% market share).

For more on Social Network Theory, see Scale-Free Networks: A Decade and Beyond by Barabasi for a pain-free summary. (Science, Vol 325, 24 July 2009; pp 412-413).

Real Social Networks:

Real social network has 3 major features:

1. Clusters (of friends who “hang out”).

2. Weak links (to your long forgotten high school classmates).

3.Hubs (politicians and others with massive number of contacts).

Figure 2: Natural social network structure with Cluster Groups

Comparing the Pareto (power law) distribution that governs SFNs, we can see that Hubs with many links (large “k”) are nodes that occur rarely whereas Clusters with few links are nodes that occur very often. Here we elaborate a mid-scale situation where certain nodes have a fair number of links and occur with some frequency – we call them “Cluster Groups”. They arise in cases where a certain Member belongs to multiple Clusters, their family cluster, work cluster, golf club cluster, etc. The same Member belongs to many Clusters that are tightly coupled leading to a Custer Group.

Failure Modes:

Failure modes of SFNs have been widely studied. The main 2 observations are that (1) SFN is robust to Failure and (2) SFN is vulnerable to attacks.

Failure means random loss of network elements such as some computers or local routers going down in the Internet. Attack refers to concerted take-down of major “hub” routers. It has been shown that removal of a small percent (15 to 20%) of “hub” routers will pull apart the network and “cascading failure” will spread (due to routers NOT under attack being unable to carry the extra load from “hub” routers) leading to total network failure.

Here are N=10 and N=100 examples; d=2 in both cases.

The N=100 example already shows some interesting features. Remember “Hubs”? One would expect the “root” node at the very top to be a Hub but the left-most node in the 2^nd level seems to be developing into a Hub with lots more “child” nodes.

Have fun with social networks!

PG

Emergent Marketing: A New Force in Social Commerce

Dr. PG Madhavan was CTO Software Solutions at Symphony Teleca Corp. Previously, he was the CTO & VP Engineering for Solavei LLC and the Associate Vice President--Technical Advisory for Global Logic Inc.  PG has 20+ years of software products, platforms and framework experience in leadership roles at major corporations such as Microsoft, Lucent, AT&T and Rockwell and startups, Zaplah Corp (Founder and CEO) and Solavei. Application areas include mobile, Cloud, eCommerce, banking, retail, enterprise, consumer devices, M2M, digital ad media, medical devices and social networking in both B2B and B2C market segments.  He is an innovation leader driving invention disclosures and patents (12 issued US patents) with a Ph.D. in Electrical & Computer Engineering.  More about PG at www.linkedin.com/in/pgmad


“Emergent Marketing” is a fundamentally new approach different from the traditional “resultant” marketing that is based on cause-and-effect at the individual level. In networks, one of the most studied phenomena is that of “infection” spread when a contagion is dropped into a network of humans; the result can be traced back to its cause – this is the hallmark of “resultant” marketing. Contra-distinct from this approach, Emergent Marketing is a low-level multi-node intervention in a human social network that creates the emergence of a ground-swell of a desirable activity (“emergent” activity) without identifiable one-to-one causality.

Let us start at the beginning. From high school Physics, we know that atoms come together to form molecules and they have palpable physical properties; for example, H2O in the form of water can flow as a liquid and you can get wet. When a state transition occurs to water (such as due to cooling), ice emerges whose “solid” property was unsuspected when H2O was a liquid – this is called an “emergent property”. Solid-state Physics has countless examples of such phenomena and one of the necessary conditions for it is densely connected simple entities. The brain is an example of such a densely interconnected neuronal network; such networks exhibit variability over time. Variability over time or dynamics is often an essential property of such networks, exemplified by the recent discovery (popularized in the press during September 2012) of the role played by “junk” DNA in the expression of “coding” DNA responsible for various diseases. There is a more informative discussion of these basic concepts in my recent blogs, “What does ‘Emergent Properties in Network Dynamics’ have to do with Shopping?”, http://pgmadblog.blogspot.com/2012/10/what-does-emergent-properties-in.html and “So-Mo-Clo Framework for CUS”, http://pgmadblog.blogspot.com/2012/07/so-mo-clo-framework-for-cus-dr.html

The last paragraph introduces three concepts: networks, dynamics and emergence. In my previous Emergent Properties blog, I noted that “Facebook connected us in a vast network – this is only a first step. The deep reason for the fascination with social networking can be understood from the shopper example. Shoppers are enmeshed in an ever-changing network of social interactions and preferences; desirable behavior can be made to emerge by perturbing the interactions within the network.”  For the first time, the concept of “Emergent Marketing” was introduced in this context.

Emergent Marketing:

As mentioned in the first paragraph, Emergent Marketing arises when one goes beyond one-to-one “resultant” marketing designed to provoke a certain purchase activity in a shopper.

A simple model to understand marketing approaches is the Purchase Funnel. The right hand side of the funnel in the figure shows the various intentions of the shopper as she traverses through the funnel. Marketing techniques aspire to move her from “Awareness” phase as quickly as possible to the “Action” or purchase phase. The left hand side shows the coarse buckets of marketing activities traditionally undertaken to achieve this funnel transition – Branding and Direct Response. By the Direct Response methods, the marketer is trying to induce a specific one-to-one response (as indicated by the word, “Direct”) that will culminate in a purchase. On the other hand, “Branding” is more nebulous; branding can take years to take hold and start to bias your purchase decisions.

When you think some more about “Branding”, it appears to have many of the features of “Emergent Marketing” that I had mentioned in the first paragraph! Branding is a multi-node intervention that creates a ground-swell of interest in a product or service but with a long delay.

In this blog, I want to focus on the Interest-Desire-Action phase of the Purchase Funnel. Ads in this phase have the desirable properties of immediacy and measureable efficacy; both are very important to the Brands that pay for advertisements. Especially, the ability to correlate ‘ad spend’ to point-of-sale receipts is a super-important metric; Brands need it (“Half of the ad expenditure produces results; the trouble is no one knows which half!”). Even during one of the worst down years of the Great Recession, worldwide advertising spending was huge (estimated at approximately $654 Billion, $54 Billion of which was for online ads); it will be good to know which of the Billions worked!

Among the many Emergent Marketing techniques possible, we want to start by building on what we already know about branding ads and create what I term “Just-in-time Branding” (JIT Branding). JIT Branding will exist in the Direct Response phase of advertising and will have immediacy and measurable efficacy.

Just-in-time Branding:

Retailer’s interest is to precipitate a specific buying behavior within a specific customer. But we do not approach it on an individual basis because we know better now - we have to consider him as a node in a network that includes his social network which creates latent influences and also his “Shopper Attribute Map” made up of his likes and dislikes.

Even though infection spread is not a good analog for Emergent Marketing, let us try to utilize it since much of the earlier work in networks has been the modeling of the spread of infections in a population. Each node has a different “influence function” – a node “infects” a varying number of other nodes (out of total of ‘N’ Nodes). If there are ‘K’ contagions, the Linear Influence (or Infection) Model (LIM) is -

v = Mi;   where M - Influence Matrix (KxN);  v – Volume of Infection (Kx1);  i – Node Infection (Nx1)

Matrix Algebra has so many powerful tools, fast algorithms and practical insights that a lot of useful information can be extracted by the expert from this simple equation. In general, singular values and vectors (and the related eigenvalues and vectors) of matrix, M, can tell you which nodes are the major “influencers” or hubs, how big their influence is and even what forms the bases of their influence in some cases! You can start populating the Linear Influence Model (LIM) with historic data collected from your real network and apply the results and insights to your business to improve or control the viral spread of your marketing message (or “contagion”).

JIT Branding using LIM is still a primitive model of true Emergent Marketing. LIM models minimally incorporate the dynamics and the ability to perturb the network in a fine-grained manner. The design and number of “contagions” for emergence of desirable “ground-swells” of activity are also open issues at this time.

What is next in Emergent Marketing?

In a “crawl-walk-run” approach to developing full-fledged Emergent Marketing techniques, JIT Branding is a “slow crawl” at best. Unlike traditional branding, our main insight is that we have to explicitly utilize the facts that (1) shoppers are embedded in social and preference networks, (2) these networks are dynamical and (3) control knobs and levers at a fine-grain node and link level have to be perturbed to engender desirable emergent activities.

One promising avenue is likely to be synchronization in dynamical networks; it is a powerful method to generate global and local “ground-swells” (sometimes with undesirable outcomes such as epileptic seizures in the brain or outages in the Internet!). More advanced Emergent Marketing techniques will exploit this avenue and other perturbation methods in dynamical social networks to create desirable short-term product affinity for a selected cohort of shoppers.

Closing the Analytics Loop:

Analytics extract meaningful patterns and information from raw data. But what do we do with those insights? The promise of Analytics will be fulfilled only when we close the loop via actions that lead to profitability in the broad sense. Emergent Marketing is an example of closing the loop of “analytics” drawn from retail data and shopper network activity back to the customer generating additional new analytics. We may have tapped a rich vein in analytics-driven retailing here; whether it will taper off or hit the mother lode remains to be seen.