Oz Shaharabani

Study topic Detailed study of network evolution by analyzing four large online social networks with full temporal information about node and edge arrivals.

What is the goal? To develop a complete model of network evolution which accurately reflects the true network in all four cases.

Study approach “the microscopic behavior of nodes solely determines the macroscopic network properties”

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.

Datasets

Notations

Preferential Attachment

1. Edge attachment by degree. 2. Edges attachment by the age of the node. 3. Bias towards node age and degree.

Preferential Attachment 1. Edge attachment by degree. 2. Edges attachment by the age of the node. 3. Bias towards node age and degree.

Edge attachment by degree

Back to our networks:

Edge attachment by degree Conclusion:

Preferential Attachment 1. Edge attachment by degree. 2. Edges attachment by the age of the node. 3. Bias towards node age and degree.

Edge attachment by node’s age

We define e(a) to be the average number of edges created by nodes of age a.

Edge attachment by node’s age We define e(a) to be the average number of edges created by nodes of age a.

Preferential Attachment 1. Edge attachment by degree. 2. Edges attachment by the age of the node. 3. Bias towards node age and degree.

Maximum-likelihood principle נראות מקסימלית - Maximum-likelihood principle היא שיטה לאומדן פרמטרים של מודל. כלומר, בהינתן התנהגות של מודל, יש לבדוק אילו פרמטרים " יסבירו " בצורה הטובה ביותר את ההתנהגות של המודל.

Maximum-likelihood principle

Bias towards node age and degree We will see four models for choosing the edge endpoints at time t. (Using the MLE principle).

Bias towards node age and degree

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

Locality of edge attachment

Notation: Edge locality of edge (u,v), it’s 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.

Locality of edge attachment

Here the distributions of these shortest path values induced by each new edge for the four networks.

Locality of edge attachment

What is the conclusion?

Locality of edge attachment Conclusion: Most of the are most likely to close triangles, i.e., connect people with common friends.

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.

Triangle-closing models

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.

Node and edge arrival process

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?

Node and edge arrival process

Node arrivals

The final network evolution model

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?

The final network evolution model Why we want to produces power law out-degree distribution? Its very important property of social network! nodes degree

The final network evolution model

Proof: (at home)

Validation of the model

Result (on FLICKER for example):

Validation of the model Result (on FLICKER for example):

Conclusions