Networks in their surrounding contexts
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![Page 1: Networks in their surrounding contexts](https://reader033.fdocuments.us/reader033/viewer/2022060118/5589e402d8b42a7b558b4693/html5/thumbnails/1.jpg)
Networks in Their SurroundingContexts
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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
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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
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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.
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produced by James Moody
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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.
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Measuring Homophily
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• 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
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Inverse Homophily
• If the probability of Cross Similarities(in this example cross gender)
greater than 2pq, then it is called as INVERSE HOMOPHILY
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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
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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.
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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
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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.
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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.
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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.
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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.
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Affiliation Networks
Bipartite Graph: We say that a graph is bipartite if its nodes can be dividedinto two sets in such a way that every edge connects a node in one set to anode in the other set
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Use of Affiliation Networks
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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
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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
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Closure Process
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Example
(i) Bob introduces Anna to Claire.(ii) Karate introduces Anna to Daniel.(iii) Anna introduces Bob to Karate.
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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?
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Example
Anna and Esther have two friends in common, while Claire and Danielonly have one friend in common. How much more likely is theformation of a link in the rest of these two cases?
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Way of finding relation
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Quantifying the effects of triadic closure in an e-mail dataset
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• 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.
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Quantifying the effects of focal closure in an e-mail dataset
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Quantifying the effects of membership closure
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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).
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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.