Networks in their surrounding contexts
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Networks in their surrounding contexts

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Simplified slides of content in chapter 4 titled "Networks in their surrounding contexts" related to information networks.

Simplified slides of content in chapter 4 titled "Networks in their surrounding contexts" related to information networks.

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    Networks in their surrounding contexts Networks in their surrounding contexts Presentation Transcript

    • Networks in Their Surrounding Contexts
    • Overview • Previously we learnt about – Different structures characterizing the social network – Typical process that affect formation of links. • Now, – Various contexts that show impact on social n/w. – Surrounding contexts: outside nodes and edges of n/w
    • Homophily • Homophily : the principle that we tend to be similar to our friends • your friends are generally similar to you along – Racial and ethnic dimensions. – Age – Mutable characteristics like • Places they live • Their occupations • Levels of influence • Interests • Beliefs • opinions
    • Example • Consider 2 cases: – A friendship that forms because two people are introduced through a common friend – A friendship that forms because two people attend the same school or work for the same company. – 1. Intrinsic to network. – 2.Beyond the network.
    • produced by James Moody
    • Triadic Closure and Homophily • B and C has a common friend A. • since we know that A-B and A-C friendships already exist • The principle of homophily suggests – B and C are likely to be similar. – there is an elevated chance that a B-C friendship will form – even if neither of them is aware that the other one knows A.
    • Measuring Homophily
    • • Homophily Test: – If the fraction of cross-gender edges is significantly less than 2pq, then there is evidence for homophily • In previous example 5 of the 18 edges in the graph are cross-gender. Since p = 2/3 and q = 1/3 • we should be comparing the fraction of cross-gender edges to 2pq = 4/9 = 8/18.(for no Homophily) But actually only 5, so homophily
    • Inverse Homophily • If the probability of Cross Similarities(in this example cross gender) greater than 2pq, then it is called as INVERSE HOMOPHILY
    • Mechanisms Underlying Homophily: Selection and Social Influence • Immutable Characteristics. – Race or Ethnicity. • Mutable Characteristics. – behaviors, activities, interests, beliefs, and opinions. – feedback effects between people's individual characteristics 1. Selection 2. Socialization and Social influence
    • Selection and Social influence • With selection, the individual characteristics drive the formation of links. • With social influence, the existing links in the network serve to shape people's (mutable) characteristics.
    • The Interplay of Selection and Social Influence • In a single snapshot of a network, It is very hard to sort out the distinct effects and relative contributions of selection and social influence. • Questions that arise: – Have the people in the network adapted their behaviors to become more like their friends? – have they sought out people who were already like them? Answers can be found through Longitudinal study of social network
    • Longitudinal study • The social connections and the behaviors within a group are both tracked over a period of time. • This makes it possible to check his – Behavioral changes that occur after changes in network connections. – Changes in network that occur after changes in individual behavior.
    • Examples • Pairs of adolescent friends to have similar outcomes – In terms of scholastic achievement – In delinquent behavior such as drug use • Normally in teenagers, both selection and social influence have a natural resonance. • Its hard to find how these two interact and how one is more strongly at work than the other.
    • Affiliation • Till now, – We have been seeing that these contexts effecting the network from outside. – It is possible to put these contexts into the network itself, by working with a larger network that contains both people and contexts as nodes.
    • Focal Points • Being part of a – particular company – Neighborhood – Frequenting a particular place – Pursuing a particular hobby or interest • Such activities can be considered as foci--The Focal points of social interaction--constituting social, physiological, legal, physical entities around which joint activities are organized.
    • Affiliation Networks Bipartite Graph: We say that a graph is bipartite if its nodes can be divided into two sets in such a way that every edge connects a node in one set to a node in the other set
    • Use of Affiliation Networks
    • Co-Evolution of Social and Affiliation Networks • It's clear that both social networks and affiliation networks change over time: • new friendship links are formed, and • People become associated with new foci. • If two people participate in a shared focus, • This provides them with an opportunity to become friends; • If two people are friends, they can influence each other's choice of foci
    • Social-Affiliation Network • As of now we have nodes for people and nodes for foci, but we now introduce two distinct kinds of edges as well. • The first kind of edge functions as an edge in a social network: it connects two people, and indicates friendship • The second kind of edge functions as an edge in an affiliation network: it connects a person to a focus, and indicates the participation of the person in the focus
    • Closure Process
    • Example (i) Bob introduces Anna to Claire. (ii) Karate introduces Anna to Daniel. (iii) Anna introduces Bob to Karate.
    • Tracking Link Formation in On-Line Data • The deeper quantitative understanding of how mechanisms of link formation operate in real life. • Exploring the previous questions in a broader range of large datasets is an important problem. • Consider triadic Closure, lets have 2 questions – How much more likely is a link to form between two people in a social network if they already have a friend in common? – How much more likely is an edge to form between two people if they have multiple friends in common?
    • Example Anna and Esther have two friends in common, while Claire and Daniel only have one friend in common. How much more likely is the formation of a link in the rest of these two cases?
    • Way of finding relation
    • Quantifying the effects of triadic closure in an e-mail dataset
    • • Forming a link each day due to 1 common friend is p(independently) • So failing to form a link is 1-p, • For K friends in common, the failing probability for k trials is (1-p)k • So probability that link forms is • This is the dotted line In previous graph.
    • Quantifying the effects of focal closure in an e-mail dataset
    • Quantifying the effects of membership closure
    • Quantifying the Interplay Between Selection and Social Influence • In Wikipedia, if we consider two editors A and B, the relation can be quantified as • For example, if editor A has edited the Wikipedia articles on Ithaca NY and Cornell University, and editor B has edited the articles on Cornell University and Stanford University, then their similarity under this measure is 1=3, since they have jointly edited one article (Cornell) out of three that they have edited in total (Cornell, Ithaca, and Stanford).
    • Conclusion • Overall, then, these analyses represent early attempts to quantify some of the basic mechanisms of link formation at a very large scale, using on-line data • But, In particular, it natural to ask whether the general shapes of the curves in previous graphs are similar across different domains – including domains that are less technologically mediated – whether these curve shapes can be explained at a simpler level by more basic underlying social mechanisms.