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Oz Shaharabani

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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.

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Maximum-likelihood principle - Maximum-likelihood principle . , , " " .

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Maximum-likelihood principle

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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):

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Conclusions

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