Social identity and Search

This is the continuation of the previous post- Its is a Small World.. Is it ?.  From the  Millgram's "Small World" experiment,the average length of the resulting chains for the letters that eventually reached the target was about six. So, if the study is correct, how can we find out such a path, among the many different possible paths in the network, So the real challenge is that even though two people are connected by a short path , how can they be able to find it. Remember that the experiment dint use a broadcast search rather a directed search.i.e., Subjects didn't pass on the letter to all the possible people they know, only the one person that they thought would know the target.
  Although broadcast search would in principle would give the shortest path to the target, it would be practically impossible. So even in theory if  we are only six degrees away from anybody else in the world, there are still 7 billion people in this world and at least as many path leading to them,how can we find the short path that we are looking for?

We can start taking best guesses at every step, if first guess is wrong or if the subsequent guesses are wrong we will end up in a blind alley. Even if we are proceeding in the right direction there is no way to know how well we are progressing .At each degree of separation we have a new decision to make and no clear way to evaluate our options. The problem with this approach is that "We are trying to solve a global problem using only the local information of the network". Though six sounds like a small number ,it is very big number when it comes to directed searches in fact anything over two is big.

Instead of focusing on just the existence of short paths , we can approach the problem by thinking how people in the network actually find those paths.People in fact have a strong notion of distance that they use all time to differentiate themselves from others. What makes the search problem feasible is that no one person has to solve it  on his own.Rather at each step, all a particular sender has to worry about is getting the message in to the next phase of search,where a phase is like a different region. In doing so, we are assuming that the next person in the chain,being closer to the target has more precise information than you do ,and so is better able to advance the search in  to the next phase.
      In order for social connections to be useful,they have to encode information about the underlying social structure[like the regions of a map]. The distance in social networks is that we can "measure" it in two different ways, social distance[in terms of how we tend to identify ourselves and others in terms of groups,institutions and activities with which we are affiliated with], which can be measured globally but which is not a true distance (and hence can yield misleading estimates); and network paths, which generate true distances but which are known only locally.

Individuals simply don't belong to groups.They also have a way of arranging them in a kind of social space so as to measure their similarity or differences with others.How they do this is , by  starting out at the the level of whole world, individuals break it down, in to a manageable number of smaller  more specific categories,subcategories so on. this continues to be like the below image.
 The distance between A and B  is the height of the lowest common-ancestor group, which in this case is three.Individuals in the same level are distance one apart.The higher up the hierarchy one has to got to find a common grouping the more distant the individuals will be.There are many kinds of distances  which we might refer when accessing the likelihood that two people will meet, Individuals in real world would derive their notions of distance from an assortment of social dimensions[geographical proximity, working in same org, studies in same college, like similar music etc.,].

Individuals A,B,C  in two dimensions. A and C are close geographically , and B and C are close in occupation. Hence, C perceives itself to be close to both A ans B but A and B perceive each other as distance. If two people are close in only one dimension consider them close even if they are quite distant in other dimensions.

        Social distance emphasizes similarities over differences. As long as individuals more likely to know other people like them ,and as long as they measure similarity along more than one social dimension,then not only will short paths exist between anyone almost anywhere , but also individuals with only local information about network will be able to find them.

          Also a surprising fact is that the best performance was achieved when the number of dimensions was only about two or three.When  everyone is using only one dimension to parse the worlds they cant take advantage of multiple affiliations to hop large distances in social space. And where everyone spread out their contacts among too many dimensions -- when none of your friends belong to the same networks-- then we are back to the world of random networks where short paths exists but can't  be found. Hence Searchable networks lie somewhere in the middle where individuals are neither too uni dimensional or too scattered.

          Efficient decentralized searches can  e conducted by means of simple, greedy algorithms providing only that the characteristics of the target element and the current element's immediate neighbors are known.A simple algorithm that combines knowledge of network ties and social identity can succeed in directing messages efficiently. The algorithm[Ref 1] is the same greedy algorithm Millgram suggested: Each member i of a message chain forwards the message to its neighbor j who is closest to the target t in terms of social distance; that is,yjt is minimized over all j ini's network neighborhood.
        The same approach of search is employed in many other disciplines like Peer-to-Peer Networks Search , distributed databases etc.,


References:
1. http://www.sciencemag.org/content/296/5571/1302.full
2. http://www.amazon.com/Duncan-J.-Watts/e/B001ILHHR4/ref=ntt_athr_dp_pel_1

Its a Small World , Is it ?- Part 1

In the this series, i will try to summarize all my learning's of the past month,about the science behind Social Networks. I must warn the readers beforehand that this might end up pretty long , but it will be definitely interesting ride and a time well spent.

So What is it ?

Small World Problem : The world when viewed as a set of acquaintances, is in a certain sense "small"  that is any one person in the world can be reached through a network of friends in only a few steps. This is named from the phrase that we often use when we usually meet stranger  in a party and find out  a mutual acquaintance, we remind each other "what a small world it is". So the Small world problem is more general . "Even When i know someone who knows you , I still know someone, who knows someone, who knows someone who does knows you".
             An experiment was conducted by Milgram in 1967, known as small world method, which is a message passing technique.He gave letters to few hundred people randomly selected from Boston and Omaha,  and the letters were to be sent to a single target person , a stock broker who worked in Boston,But the letters came with a unusual rule, Recipients were to send the letters only to somebody who knew on a first name basis. i.e., If the recipient knows the target person directly he can sent it to him or if he doesn't know, he has to send it to the someone who they did know who they thought as someone closer to the target .
When asked people how many steps would it take to reach the recipient, most of them thought it would be in hundreds, bu the result was a surprising six (yes 6), hence the famous phrase "Six degrees of Separation - Everybody on this planet is separated by only six other people".
           If we try to do an reasoning on this, mathematically   it is like a pure branching network, Let say if I know only 5 people.but within two degrees of separation , I can reach 25, within three degrees 105, and so on.. Scaling this this 100 friends, within 6 steps i can easily connect myself to the entire population of the planet. So maybe its obvious it sis a really small world.

Six Degrees-Branching network

          But there is a fatal bug in the above reasoning. Think about your 10 best friends, and ask yourself who their ten best friends would be , Chances are you would come up with the same people , this feature is called clustering, which is really just to say that most people friends are also some extent friends of each other. This how social networks are in general, little clusters based on location, interests joined to each other by the overlaps created  when individual belonging to one group also belong to another group.

Actual Social network

This characteristic of a networks is particularly relevant to the small world  problem,the more your friends know each other , the less use they are to connect to someone who you really don't know.The paradox of the social networks that Millgrams experiment highlighted is that, on one hand the world is highly clustered,yet on the other hand we can still manage to connect to anyone at all in a very few small steps.
     
  After 30 years of this experiment, the actual nature of the world remained in question,and the paradox at its heart remained just that ,a paradox. however recent works has helped  to resolve the "Small world phenomenon". The idea that broke the stalemate was found by coming at the old problem with a new direction.Rather than going out in to the world and measuring it , we can construct a mathematical model of the social network and solve with the power of "Computers and Mathematics".

  Too much for intro.. next part I will write about the representing the model and understanding the basic properties of such models(Its all about Graphs :-)).

A Bored Master and a lost student !!!!

          So why a technical blog now..As mentioned in the title of this post, I always felt there are two faces of every programmer[Aparichit :-)], one the master and the other student, As we move on with our career, the student kind of becomes invisible[someone calls removeChild()] and the master takes off , and thats is the most vulnerable hole(like a goto statement :-)). 

 Yesterday i have completed my six year milestone in my Programming career, and thinking back at what i did all these years after college, kind of makes me feel confusing . My first two years and last two years have been the best till now[thanks to my colleagues] and the other two years kind of just passed on without doing anything valuable. So now trying to give a much needed push/kickstart my learning desire again and bring the student back again in to focus(addToStage() :-) too much flex coding i guess).How is now different from college ?
                  
               Back then college had ben like a military academy, and what little knowledge had seeped through the cracks of every student preoccupations seemed of little relevance in the real world now.I had started this reimaging upteen times but everytime  i start it, All the textbooks I read i get the obvious stuff , and after some futile struggling with the rest, convinced myself it wasn't very intersting anyway. Hmm.. This time should be better and hopefully long lasting :-), and this blog would keep me reminding my journey and progress towards "THE BIG THING :-)" !!!!!