Patterns And A Generative Model Jan 24, 2014 Authors: Jianwei Niu, Wanjiun Liao, Jing Peng, Chao...

Patterns And A Generative Model

Jan 24, 2014

Authors: Jianwei Niu, Wanjiun Liao, Jing Peng, Chao Tong

Presenter: Guoming Wang

Published: Performance Computing and Communications Conference (IPCCC), 2012 IEEE 31st International

Nanyang Technological University |

Outline

▪ Introduction

▪ Definitions And Properties

▪ Observations

▪ Model


Temporal evolution of social networks

▪ How do social network evolve through network?

▪ How do the different components of an entire network form and die?

▪ Is the second largest component in a network really very small in size?

Temporal evolution of social networks has attracted considerable interest among researchersTemporal evolution of social networks has attracted considerable interest among researchers

Nanyang Technological University | 4

Method

Empiricalobservations

Analyze the mergings

Proposemodel? !

Problem Future work

Two types of mergings: 1. mergings between the disconnected components themselves2. Mergings between the disconnected components and the giant component

Datasets studied


Definitions and interested Properties

G = (V, E)

Graph G consists of a set of nodes V and a set of edges E.

GCC

Final size of the DCs

The typical directed networks can be stated By a “bow-tie” structure, and usually have a giant connected component(GCC) which involves a significantly large fraction of nodes

The number of nodes in that DC when it dies. It reveals how large DCs can grow before dying out

1

4DC

Longevity of DCs

The disconnected components(DC) of a network are defined as the small components that are not connected to any other components in the network

The length of the period from the birth of a DC to its death. It reflects how long the DCs can live before they merge with other DCs

2

3

What properties or patterns can we obtain from the temporal

evolution of DCs ?


Observation1

Longevity distribution of DCs in each datasetAll plots demonstrate a decaying trend, and after the vertical line x = k, the curves begin to oscillate apparently. The units of the longevity values are in snapshots.The longevity of each DC counts the number of snapshots that such a DC can live in the observation period of each dataset.


Observation2

Final size distribution of DCs in each dataset. The fitted lines and the slopes are shown. The plots demonstrate power laws


Observations

• Observation1

• The curve of the overall DC longevity distribution shows a

decaying trend, with oscillations at the tail , indicating that

the short-lived DCs account for a large fraction of all the

DCs, and the longevity of long-lived DCs do not follow a

simple fixed pattern.

• Observation2(Final Size Power Law(FSPL))

• Let sc denote the final size of a disconnected component,

and let nc denote the number of disconnected components

whose final size are sc. Then nc and sc follow a power law

with exponent B


Longevity distribution of DCs that are absorbed by GCC

The trend of the curves revealing the similarity between these distributions and the overall longevity distribution shown previously.Which can be regarded as a hint that the majority of DCs are absorbed by the GCC.


Final size distribution of DCs that are absorted by GCC

The fitted lines and the slopes demonstrate again the FSPL and similarity between these distributions and the overall final size distribution


Longevity distribution of DCs that merge with other DCs

The curves show a decaying trend, where short-lived DCs are common. There are still small spikes in the decaying part of the curves, and after that, the curves enter a relatively stable state.


Final size distribution of DCs that merge with other DCs


Different timestamp


Mergings of Disconnected Components

A DC can either be absorbed by the GCC, or merge with other DCs;The target is to know if there is an obvious difference in number between these two types of mergings

Number of DCs is much less compared with the mergings involving the GCC.

Long-lived DCs are seldom involved in the DC mergings

The count of DCs decreases as the longevity value increases.


Observation3

• The mergings among DCs are all

small in size, and specially most

of the mergings happen between

two DCs.


Proposed Model

▪ The decaying trend in DC longevity distribution

▪ The FSPL in the final-size distribution of DCs

▪ The small merging sizes


Surfer Model – generative steps

1. v chooses a host node u uniformly at random from all the existing nodes in the network, and forms a link to u

2. Generate a random number count which is geometrically distributed with expectation pfrnd/(1-pfrnd).Node v randomly chooses count edges of u expect the edge as it can if there are not enough edges.

3. Let x1, x2…xk denote the nodes on the other ends of these chosen edges in step(2). Node v forms links to x1, x2…xk, and then goes to step(2), recursively visiting all these nodes


Surfer Model – Generative steps depiction


Pseudo code


Conclusion and Future work

Empirical observations and analyse longevity

and final sizeof DC

Detecting anomalies and forcasting the

future states…?

Surfer model

Longevity: decaying trend

Final-size: power law


Thank you – Enjoy the rest of your night

Patterns And A Generative Model Jan 24, 2014 Authors: Jianwei Niu, Wanjiun Liao, Jing Peng, Chao...

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