A brief introduction about SNA

     In my viewpoint, what called social network analysis can have two ways to describe: one of them is relationships and flows between different entities such as people, groups, organizations, computers, URLs.
     Another refers to methods used to analyze social networks, social structures made up of individuals , which are connected by one or more specific types.
     Social network analysis views social relationships in terms of network theory consisting of nodes and ties . Nodes are the individual actors within the networks, and ties are the relationships between the actors. In its simplest form, a social network is a map of specified ties, such as friendship, between the nodes being studied. The nodes to which an individual is thus connected are the social contacts of that individual.
     Social network analysis provides both a visual and a mathematical analysis of human relationships.In the example, we have the following picture:

     So, when it comes to the question in the example, we first briefly describe the simple social network in the following chart:

	Alice	Bob	Carol	David	Eva
Alice	-	1	1	1	0
Bob	1	-	0	1	0
Carol	1	0	-	1	0
David	1	1	1	-	1
Eva	0	0	0	1	-

    In the above charts, we have following assumptions:the links between two people means that they knew each other and they cannot knew the other guys if there is no direct link between two. In the chats that 1 means link and 0 is no link which means they do not know each other.
    Within the question about who is the most influential point, we can easily see that from the picture and chart that David is, but what is the standard to do the determine?
    We have several methods to measure a social network, different methods give us different point of view about that special social network. We learned from the lecture that we have degree, density, geodesic distance and centrality to measure the social network.

     According to my opinion, to measure the most influential, the notion of influence range first comes to my mind, to find out whether it is suitable for the question, we have the following about the notion:
     Define influence range of ni as the set of actors who are reachable from ni
     Define Ji as the number of actors in the influence range of actor i (excluding i itself)
     An “improved” actor-level centrality closeness index considers how proximate ni is to the actors in its influence range
     A refined closeness centrality (for both directional and nondirectional) is

     This index is a ratio of the fraction of the actors in the group who are reachable, to the average distance that these actors are from the actor ni
So, we can easily computing the results in the following chart:

Alice	0.75
Bob	0.5
Carol	0.5
David	1
Eva	0.25

     
    From the result, we take David as the most influence node in this social network.
    But we should also keep in mind is that: is it a good way to measure this example in that way? The answer is no!
    we have one reason that in this example, we have no distance meaning, so the computing result may have not show the result correctly.
    So we turn to other ways to do the research:  centrality.
    We have three centralities: Degree, Betweenness,Closeness. To define which to use, we first see the differences between them:
    Degree Centrality:It signifies activity or popularity
    Betweenness Centrality: It is a measure of the potential for control as an actor who is high in “betweenness” is able to act as a gatekeeper controlling the flow of resources (information, money, power, e.g.) between the alters that he or she connects.
    Closeness Centrality: Can be understood as how long does it take for a message to spread inside the network from a particular node
    Backing to our question, we found that the degree centrality is the best to fit the question, so using this to compute, we have the following results:

Alice	3
Bob	2
Carol	2
David	4
Eva	1

    What we get the answer is the same form the above but I think this is more reliable than the first one, and we can also use other methods to do the same question, due to the limited time, I think if you are interested, you can do it !
    According to the above resulted are obtained, I found the following findings:
    1. Different social networks may have different characteristics, if we want to know furture about it, the metheds we use to do the research should follow the special characteristics, though sometimes the results maybe the same.
    2.One same social network, using different methods may lead to different results, this is quiet normal.
    3.Due to the limition of one social network, some notion of the methods may have no meaning, such as the distance in the example.
    4. We can do one research in the social netork by using different assumptions, may have differnet results, this is the same as view one thing in differnet views.
    5. As we can easily see that the cutpoint is David and the bridge is the tie between David and Eva, so we can draw a conclusion: the most influence point maybe or near the cutpoint or the bridge.


Reference:
 http://www.orgnet.com/sna.html
 http://en.wikipedia.org/wiki/Social_network_analysis