Doing the Real Math of Recruiter Networks

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“For strange effects and extraordinary combinations we must go to life itself, which is always far more daring than any effort of the imagination.” –Arthur Conan Doyle, creator of “Sherlock Holmes”

Where Trees Meet Rivers


Do you have any idea of how many 2-person contacts among your recruiter network are possible?  More importantly, do you know the professional, social and IT implications of that number?

The natural tendency is to appraise a network by its number of members and to map that growth as a simple line or curve of membership against time. However, correlated with that growth of membership is a far more rapid increase in connections among the members. This second kind of growth is exponential and mind-boggling, with implications that transcend monetization of such networks or their social, professional or political clout gauged merely by network size.

Bulking up Through Combinations

Take the simplest possible cases as illustrations of this process: If your network consists of only two people, then the result in this case is the only instance in which the number of members equals the number of connections. As soon as you have three people as members, the 2-person connections increase to three. With four people, those 2-person connections increase to 6. If you add in the 3-person connections among those 4 people, that yields another 4. Including 4-person connections, that adds one more, for a total of 11. If none connects with any of the others, that adds one more way in which the network can function, for a total of 12.

So, what about a LinkedIn network with, say, 100,000 members?  (Note: Hate math? Skip the rest of this paragraph.) If you want to work that out and calculate all possible connections, e.g., 2, 3, 4….5,000…..50,000….100,000 at a time, here’s the handy formula for doing so: ?C(n,k) =? n!/k!(n-k)! , where n= the total number, viz., 100,000; k= the number at a time, e.g., 20;, where n!= the product of numbers, beginning with n, multiplied by the next smaller number, e.g., 4!= 4x3x2x1. The “sigma”, summation sign, means you have to do the calculation for every one of the possibilities from 0 to k and then add them up, e.g., 1 person, 2 people at a time, 3 people at a time…..up to an including 100,000 people at a time (which is the easiest calculation: exactly 1 way). Having completed the 100,000 calculations, you then sum all of them (excluding the zero case.

Fortunately and unfortunately, there are lots of online calculators that will instantly do the calculation for you, but only up to 1,000-person group and for only a specific number at a time, e.g., all possible10-person connections among 1,000 = 263,409,560,461,970,212,832,400 (source: What’s fortunate is that they are available; what’s unfortunate is that they are limited as described.

Anyway and obviously, the number of possible connections is staggering. Remember, that enormous number in the previous paragraph is only one of 1,000 totals to be calculated for the 1,000-person network. I would say, “You can imagine the rest”, were it not for the fact that you can’t. Conceive the rest—possibly; imagine—impossible, i.e., to try to picture these numbers in some concrete way.

What are the implications for you, as a recruiter, of these incomprehensibly numerous possible connections?

Transforming Quantity into Quality

Here are some:

1.   Trees vs. Rivers: As the total membership increases, so does the likelihood of the formation of intra/inter-sub-networks, organized around common interests, professional focus, recruiting and other issues. The more people there are in any one network, the likelier it is that they will form sub-networks. These sub-networks should not be regarded only as twigs on a  network tree, or twigs and sub-branches on a non-growing tree diagram—even though some of them can emerge and take that form, like sub-committees within a fixed-size organization.

In this non-growing tree model, adding sub-committees does not represent a growth in membership numbers. Such an intra-network “sub-committee” model will accurately describe many such k-person sub-networks, but not all of them.

The reason that this tree model is insufficient is that, in many instances, sub-networks will overlap with networks and sub-networks established outside their original recruiter network, e.g., skim-boarder, MBA, accountant and Californian networks.

Call these “inter-network committees”, on analogy with the intra-network “sub-committees”. Think of how river channels diverge from their main source and then link up with and criss-cross others generated by another source. Then imagine these dynamic networks intersecting a static tree-structured network, e.g. a political party or corporation and their top-down decision and organizational flows.

What should impress you in all of this, besides the explosion in total numbers of connections, is the clear relevance of the systems theory principle “transformation of quantity into quality”.

For example, if enough apparently invisible threads are woven together, vivid color will gradually and eventually appear, as an “emergent” quality in a silk scarf.

Understanding this principle, we can reasonably predict that some as yet unforeseen “emergent” qualitative changes and properties will eventually emerge from not only the sheer size of the primary networks, but also from their staggering number of sub-connections and emerge as big surprises.

2. Emergence of a popular (semantic) web search capability that allows immediate identification of all intra- and inter-subgroups (of interest to you). Imagine you are a recruiter, a Californian and that you have an MBA. You type in these categories as keywords. Hit enter and a listing of all Californian MBA recruiters appears. Alternatively, you can select an “OR” function and a list of all Californians, all skim-boarders and all MBAs within your primary network appears.

I tried that on Google, as follows: “’recruiter’ AND ‘California’ AND ‘MBA’ AND ‘skimboarder’. Here are the only two results:

Google Search Results:  2 results (0.22 seconds):

  • “What’s your name Dude?” – Mad Dog Tannen [Archive] – League of .I am 27 and work in Human Resources as a recruiter for a major defense contractor …… I am working on a Masters of Science in Management and then an MBA. … – Cached
  • twibs – kellyrfeller on Twitter – books, online, Skimboarder. Surfer. Hippie. Music Lover. A Lot Crazy. …. Bio: MBA, Director of Channel Partner Development with AIS Media, an award winning interactive …… – Cached

Clearly, this cannot reflect the true overlap among the three keyword groups.

The same search, but without the “AND” turned up 14,800 mixed and generally only partially relevant results, including this useful gem: “Vancouver pooch skimboards into Rose Bowl”.

On the other hand, “’Recruiter’ OR ‘California’ OR ‘skimboarder’ OR ‘MBA’” yielded 3.3 billion results, which is too unwieldy a number and too far off the mark to be useful

The implication is clear: As recruiting, social and other networks have increased in size, the critical mass required to inspire, support and deploy the technological advances that will facilitate precise and accurate subgroup identification and communication will be achieved, if it hasn’t been achieved already. It’s a matter of “when”, not “whether” the corresponding technology will be widely implemented.

3.   Emergence of “cloud” networking: This means that you will be able to directly access individual members of intra/inter-subgroups without having to link in directly to their host networks, such as LinkedIn, Facebook or any specific recruiting site. This one, too, is but a matter of time.

4.   Pruning and seeding: Using the intra-network subgroup tree model as a paradigm, it can be readily seen that like an overgrown tree or one bursting with seeds, some of that mass will ultimately be pruned or shed.

Some of the initial network members will be pruned away, e.g., by conflicting demands on their time or by greater attraction to another network; others will function as primary network seeds to be planted in other networks.

What is quite interesting to speculate upon is what the ratio of pruned members to seed members will evolve toward in any given network and what dynamical features tip the scales in one direction rather than the other.

Among the factors that may contribute to a higher proportion of seeding than of pruning, of course there are the obvious differences between competing networks in terms of their appeal.

Much less obvious is the potential influence of “reciprocal overlap”. This  occurs when the rival network’s members not only have something in common with the primary network’s member who has joined them (because he has a significant one-to-many mapping of interests from himself to them), but also individually and collectively have something (else) in common with a substantial number of the primary network’s members (a “one-to-many” or ”many-to-many” mapping.

Such mappings are like the mapping of one reservoir to many households or the mapping of many wells to many households, with each well serving many homes and each home drawing water from more than one well, respectively.

Implicit in this concept of a 2-way flow is the suggestion that any primary network’s organizer should encourage ties with organizations or networks that complement the primary network in one of two ways:

  • The secondary independent network is virtually non-competing, yet substantially overlapping (many-to-many mapping of members and interests)
  • The secondary independent network is virtually non-competing, and mostly non-overlapping in terms of members (one-to-many mapping of primary member to secondary network members) and virtually no mission overlap.

An example of the first would be a recruiter network whose members join a couch-surfer network: many members of the recruiter network could connect with, as well as be members of the couch surfer, or frequent-flier, AARP, etc. networks and vice versa.

An example of the second and non-overlapping networking is a recruiter network whose individual members join, in very small numbers, disparate non-competing networks/

Examples include  a chamber of commerce network, a skimboarder network, “Accountants without Borders” , or even TV sit-com star Roseanne Barr’s “Green Tea Party”  presidential candidacy for fed-up political and environmental activists.

The network pairing of two non-competing networks with high overlap can offer immediate and obvious cross-dividends—in terms of expanded memberships reflecting demographic, interest or mission overlap.

On the other hand the low-overlap pairings of disparate networks can serve as platforms and bases from which additional networks can be indirectly and perhaps more slowly penetrated as a result of word-of mouth/email and other communications spinoffs.

To assume that the primary measure of a network—recruiting or otherwise—is its size is to vastly underestimate the significant role of the incredibly  more numerous connections among its members as a catalyst of qualitative technological, professional and social change.

Likewise, to imagine that these large numbers will only trigger a “chain-reaction” is to risk a second underestimation, by confusing the actual potential linkages with nuclear fission or a ping-pong balls-on-mousetraps chain reaction in a small room.

Those kinds of chain reactions map one ball or one atom into only two or several others. In the recruiter network, one member can map himself into all of the other members—a chain-reaction of a much higher order.

At the same time, such underestimation of the role and scope of member-to-member interactions may contribute to being oblivious to potential or looming problems emerging from these mind-bogglingly huge numbers of potential and executed links. You say, “What problems?”

The most obvious problem is that which Alvin Toffler, more than 40 years ago, in his now-classic best-seller, Future Shock, called “over-choice”, designating, in this context, having more choices available than can comfortably and thoroughly be weighed and filtered.

Buridan’s But

There are two circumstances in which it is difficult or impossible to choose: The first is a simple forced choice between two or more identical things.

This dilemma is best illustrated by the quandary of “Buridan’s Ass”—named after French moral philosopher, Jean Burridan and referring to a famished donkey forced to choose between two identical stacks of hay (or positioned at equal distances from hay and water, when as hungry as it is thirsty).

Call the donkey’s dilemma a form of “under-choice”, comparable to having no choice at all, i.e., one or zero alternatives. The donkey’s logical dilemma is this: If the stacks are truly identical or equally tempting, lacking even a left-side/right-side bias, logic suggests the donkey will starve (or die of thirst).

But if the donkey chooses, this contradicts the assumption that they were absolutely identical, indistinguishable and equally irresistible.

The donkey’s practical dilemma is in being torn between two equally compelling choices.

A smart donkey would resolve this by always having a coin to toss.

The second way in which it becomes increasingly difficult, if not impossible to comfortably and in an informed way choose, is the situation of “over-choice”, in which there are simply too many choices, e.g., a buffet with 2,000 dishes or night clubs with 2,000 singles.

One response of the mind is to simply hesitate to choose, or even to give up, as the addition of more choices diminishes the value of each.

It is not hard to imagine that many people (have or) will quit Facebook when they realize(d) that their own Facebook pages shrank into insignificance at somewhere around the 400 million registrant mark.

It is also not hard to imagine just as many getting “Facebook fatigue”, having to choose whom to visit, whom to allow to visit, whose photos to post, how much time, space and energy to allocate and divvy up among Facebook “friends”, etc.

The actual and projected numbers of these losses and the long-term trend are in all likelihood known to the Facebook statisticians. What remains to be seen is how long new-member registrations will more than offset such losses, i.e., what the long-term ratio of those pruned to those who act as seeds or roots will be.

Precisely the same question can be asked of recruiter networks as their numbers and intra/inter-subgroups grow. Which will prevail? The pruning, the seeding or the rooting?

For now, hope for the best….

….and knock on wood.

Read more in Social Network

Michael Moffa, writer for, is a former editor and writer with China Daily News, Hong Kong edition and Editor-in-chief, Business Insight Japan Magazine, Tokyo; he has also been a columnist with one of Japan’s national newspapers, The Daily Yomiuri, and a university lecturer (critical thinking and philosophy).