Study topic Detailed study of network evolution by analyzing
four large online social networks with full temporal information
about node and edge arrivals.
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What is the goal? To develop a complete model of network
evolution which accurately reflects the true network in all four
cases.
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Study approach the microscopic behavior of nodes solely
determines the macroscopic network properties
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Model core processes 1. Node arrival process - governs the
arrival of new nodes into the network. 2. Edge initiation process -
determines for each node when it will initiate a new edge. 3. Edge
destination selection process -determines the destination of a
newly initiated edge.
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Datasets
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Notations
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Preferential Attachment
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1. Edge attachment by degree. 2. Edges attachment by the age of
the node. 3. Bias towards node age and degree.
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Preferential Attachment 1. Edge attachment by degree. 2. Edges
attachment by the age of the node. 3. Bias towards node age and
degree.
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Edge attachment by degree
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Back to our networks:
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Edge attachment by degree Conclusion:
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Preferential Attachment 1. Edge attachment by degree. 2. Edges
attachment by the age of the node. 3. Bias towards node age and
degree.
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Edge attachment by nodes age
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We define e(a) to be the average number of edges created by
nodes of age a.
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Edge attachment by nodes age We define e(a) to be the average
number of edges created by nodes of age a.
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Preferential Attachment 1. Edge attachment by degree. 2. Edges
attachment by the age of the node. 3. Bias towards node age and
degree.
Bias towards node age and degree We will see four models for
choosing the edge endpoints at time t. (Using the MLE
principle).
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Bias towards node age and degree
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We conclude that PA (model D) performs reasonably well compared
to more sophisticated variants based on degree and age. i.e.,the
probability of selecting a node v is.proportional to its current
degree
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Locality of edge attachment
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Notation: Edge locality of edge (u,v), its the number of hopes
its span. i.e., the length of the shortest path between nodes u and
w immediately before the edge was created.
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Locality of edge attachment
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Here the distributions of these shortest path values induced by
each new edge for the four networks.
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Locality of edge attachment
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What is the conclusion?
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Locality of edge attachment Conclusion: Most of the are most
likely to close triangles, i.e., connect people with common
friends.
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Triangle-closing models Given that such a high fraction of
edges close triangles, we aim to model how a length-two path should
be selected. We will see five models of choosing neighborhood
node.
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Triangle-closing models
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We will focus on random-random model because: Gives higher
probability to nodes with more length-two paths. (therefore, its
biased towards high-degree nodes). Gives a sizable chunk of the
performance gain over the baseline (10%). Much simple then the
other models.
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Node and edge arrival process
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We want to create an optimal model, but we have to answer some
questions before: Which nodes initiate edges? How long a node
remains active in the social network? What are the specific times
at which the node initiates new edges?
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Node and edge arrival process
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Node arrivals
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The final network evolution model
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We now show that our model, node lifetime combined with gaps,
produces power law out-degree distribution. Why we want to produces
power law out-degree distribution?
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The final network evolution model Why we want to produces power
law out-degree distribution? Its very important property of social
network! nodes degree
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The final network evolution model
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Proof: (at home)
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Validation of the model
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Result (on FLICKER for example):
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Validation of the model Result (on FLICKER for example):