temporal distance metrics for social networks analysis
play

TemporalDistanceMetricsfor SocialNetworksAnalysis JohnTang 1 , - PowerPoint PPT Presentation

TemporalDistanceMetricsfor SocialNetworksAnalysis JohnTang 1 , MircoMusolesi 1 ,CeciliaMascolo 1 andVitoLatora 2 ComputerLaboratory,UniversityofCambridge 2


  1. Temporal
Distance
Metrics
for
 Social
Networks
Analysis
 John
Tang 1 ,
 Mirco
Musolesi 1 ,
Cecilia
Mascolo 1 
and
Vito
Latora 2 
 Computer
Laboratory,
University
of
Cambridge
 2 INFN/Dept
of
Physics,
University
of
Catania


  2. Credit:
Mark
Newman
 mirco.musolesi@cl.cam.ac.uk
 2


  3. hhhCredit:
kc
claffy,
CAIDA
 hhhHyperbolic
view
of
BGP
tables
 mirco.musolesi@cl.cam.ac.uk
 3


  4. Reality
Mining
Dataset
 mirco.musolesi@cl.cam.ac.uk
 4


  5. mirco.musolesi@cl.cam.ac.uk
 5


  6. Credit:
Flutracker.com
 mirco.musolesi@cl.cam.ac.uk
 6


  7. Problem :
existing
metrics
do
not
capture
the
 inherent
dynamism
of
networks
over
time.
 We
need
new
 temporal
metrics
 defined
over
 temporal
graphs
 for
studying
dynamic
 processes
over
these
networks.
 mirco.musolesi@cl.cam.ac.uk
 7


  8. An
Example
of
Temporal
Graph
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 8


  9. …and
the
Corresponding
Static
Graph
 A
 B
 C
 D
 E
 F
 mirco.musolesi@cl.cam.ac.uk
 9


  10. INFOCOM
(2nd
day)
 mirco.musolesi@cl.cam.ac.uk
 10


  11. mirco.musolesi@cl.cam.ac.uk
 11


  12. Calculating
the
Temporal
Distance

 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 12


  13. Calculating
the
Temporal
Distance
 (t
=
1)

 D
at
distance
1
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 13


  14. Calculating
the
Temporal
Distance

 
(t
=
2)
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 14


  15. Calculating
the
Temporal
Distance

 
(t
=
3)
 B
and
C
at
distance
3
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 15


  16. Calculating
the
Temporal
Distance

 
(t
=
4)
 F
at
distance
4
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 16


  17. What
about
the
Static
Distance?
 A
 B
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 E
 F
 E
is
 statically 
reachable
but
in
reality
it
is
not
 dynamically 
reachable!
 A‐>
F
requires
2
transmissions
(hops),
but
in
reality
it
requires
3
 No
information
about
the
duration
of
the
process
 mirco.musolesi@cl.cam.ac.uk
 17


  18. What
about
the
Symmetric
Distance

 (F
to
A)?
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 18


  19. Calculating
the
Inverse
Temporal
Distance
 (t
=
1)
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 19


  20. Calculating
the
Inverse
Temporal
Distance
 (t
=
2)
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 20


  21. Calculating
the
Inverse
Temporal
Distance
 (t
=
3)
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 21


  22. Calculating
the
Inverse
Temporal
Distance
 (t
=
4)
 A
is
not
reachable
 
[infinite
distance]
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 22


  23. Let’s
Get
a
Bit
More
Formal…
 • Characteristic
temporal
path
length:
 • Defined
considering
the
horizon
of
the
 infection
 • Possible
problem
due
to
the
potential
 divergence
due
to
pairs
of
nodes
that
are
not
 temporally
connected
 mirco.musolesi@cl.cam.ac.uk
 23


  24. Let’s
Get
a
Bit
More
Formal…
 • Characteristic
temporal
path
length:
 • Defined
considering
the
horizon
of
the
 infection
 • Possible
problem
due
to
the
potential
 divergence
due
to
pairs
of
nodes
that
are
not
 temporally
connected
 mirco.musolesi@cl.cam.ac.uk
 24


  25. Impact
of
the
Horizon
Parameter
 (F
‐>
A,
h
=
1)
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 25


  26. Impact
of
the
Horizon
Parameter
 (F
‐>
A,
h
=
2)
 A
was
not
reachable
at
all
with
h
=
1
(in
4
time
windows),
but
with
h
=
2
it
is
a
distance
1!
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F
 t
=
2
 t
=
1
 t
=
3
 t
=
4
 mirco.musolesi@cl.cam.ac.uk
 26


  27. Let’s
Get
a
Bit
More
Formal…
 • Characteristic
temporal
path
length:
 • Defined
considering
the
horizon
of
the
 infection
 • Possible
problem
related
to
the
potential
 divergence
due
to
pairs
of
nodes
that
are
not
 temporally
connected
 mirco.musolesi@cl.cam.ac.uk
 27


  28. Let’s
Get
a
Bit
More
Formal…
 • Solution:
definition
of
temporal
efficiency:
 • High
value
of
E
(low
value
of
L)
means
that
the
 nodes
of
the
graphs
can
communicate
efficiently
 mirco.musolesi@cl.cam.ac.uk
 28


  29. Local
Temporal
Efficiency
 Node
i
 A
 B
 D
 C
 E
 F
 mirco.musolesi@cl.cam.ac.uk
 29


  30. Temporal
Clustering
Coefficient
 Node
i
 A
 B
 D
 C
 E
 F
 mirco.musolesi@cl.cam.ac.uk
 30


  31. INFOCOM
Dataset:
 Static
vs
Temporal
Metrics
 H=wfwf
 h min
 =
12am,
h max 
=
12pm,
w
=
5
min
 Static
metrics
underestimate
L
 mirco.musolesi@cl.cam.ac.uk
 31


  32. Reality
Mining
Dataset
 h
=
1,
tmin
=12
am,
tmax
=
12pm,
w
=
5
min
 h
=
1,
t min 
=12
am,
t max 
=
12pm,
w
=
5
min
 mirco.musolesi@cl.cam.ac.uk
 32


  33. Variation
of
the
Clustering
Coefficient
 over
Time
 Reality
Mining
Dataset
(t min 
=
12
am,
t max 
=
12
pm,
w
=
5
min)
 mirco.musolesi@cl.cam.ac.uk
 33


  34. Temporal
Efficiency
vs
Static
Efficiency
 MIT
Dataset
 mirco.musolesi@cl.cam.ac.uk
 34


  35. Current
Research
Agenda
 • Centrality
measures
 • Study
of
dynamic
processes
over
the
 networks:
 – Message
dissemination
 – Epidemics
 – Information
propagation

 • Analysis
of
new
and
larger
datasets
 • Small‐world
behavior
in
temporal
networks
 mirco.musolesi@cl.cam.ac.uk
 35


  36. Summary
of
the
Talk
 • New
temporal
metrics
for
studying
dynamic
 processes
over
dynamic
networks
 – Temporal
distance
 – Temporal
efficiency
 – Temporal
clustering
 • Analysis
using
real
datasets
 mirco.musolesi@cl.cam.ac.uk


  37. Questions?
 Mirco
Musolesi

 mirco.musolesi@cl.cam.ac.uk
 [soon
to
be:
mirco@cs.st‐andrews.ac.uk]
 http://www.cl.cam.ac.uk/~mm753
 mirco.musolesi@cl.cam.ac.uk
 37


  38. INFOCOM
Dataset:
 What
Happens
if
We
Reshuffle
the
Sequence?
 h
=
1,
t min 
=12
am,
t max
 =
12pm,
no
runs
=
50
 mirco.musolesi@cl.cam.ac.uk
 38


Recommend


More recommend