Download Temporal evolution of social networks

Patterns And A Generative
Model
Authors: Jianwei Niu, Wanjiun Liao, Jing Peng, Chao Tong
Published: Performance Computing and Communications
Conference (IPCCC), 2012 IEEE 31st International
Presenter: Guoming Wang
Jan 24, 2014
Outline
▪ Introduction
▪ Definitions And Properties
▪ Observations
▪ Model
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Temporal evolution of social networks
Temporal evolution of social networks has attracted
considerable interest among researchers
▪
▪
How do social network evolve through network?
▪
Is the second largest component in a network
really very small in size?
How do the different components of an entire
network form and die?
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Method
?
Two types of mergings:
1. mergings between the disconnected components
themselves
2. Mergings between the disconnected components
and the giant component
Empirical
observations
Analyze the
mergings
Propose
model
Problem
!
Future
work
Datasets studied
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Definitions and interested Properties
Graph G consists of a set of nodes V and a set of edges E.
G = (V, E)
1
GCC
3
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
2
DC
The disconnected components(DC) of a
network are defined as the small
components that are not connected to any
other components in the network
Longevity of DCs
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
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Final size of the DCs
The number of nodes in that DC when it
dies. It reveals how large DCs can grow
before dying out
What properties or patterns can
we obtain from the temporal
evolution of DCs ?
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Observation1
Longevity distribution of DCs in each dataset
All 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.
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Observation2
Final size distribution of DCs in each dataset.
The fitted lines and the slopes are shown. The plots demonstrate power laws
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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
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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.
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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
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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.
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Final size distribution of DCs that merge with other DCs
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Different timestamp
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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.
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Observation3
• The mergings among DCs are all
small in size, and specially most
of the mergings happen between
two DCs.
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Proposed Model
▪ The decaying trend in DC longevity distribution
▪ The FSPL in the final-size distribution of DCs
▪ The small merging sizes
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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/(1pfrnd).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
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Surfer Model – Generative steps depiction
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Pseudo code
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Pseudo code
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Conclusion and Future work
Empirical
observations and
analyse longevity
and final sizeof DC
Surfer model
Longevity:
decaying trend
Final-size: power
law
Detecting
anomalies and
forcasting the
future states…?
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Thank you – Enjoy the rest of your night
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