TemporalDistanceMetricsfor SocialNetworksAnalysis JohnTang 1 , - - PowerPoint PPT Presentation

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temporal distance metrics for social networks analysis
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TemporalDistanceMetricsfor SocialNetworksAnalysis JohnTang 1 , MircoMusolesi 1 ,CeciliaMascolo 1 andVitoLatora 2 ComputerLaboratory,UniversityofCambridge 2

slide-1
SLIDE 1

Temporal
Distance
Metrics
for
 Social
Networks
Analysis


John
Tang1,
Mirco
Musolesi1,
Cecilia
Mascolo1
and
Vito
Latora2
 Computer
Laboratory,
University
of
Cambridge


2INFN/Dept
of
Physics,
University
of
Catania


slide-2
SLIDE 2

mirco.musolesi@cl.cam.ac.uk
 2


Credit:
Mark
Newman


slide-3
SLIDE 3

hhhCredit:
kc
claffy,
CAIDA
 hhhHyperbolic
view
of
BGP
tables


3
 mirco.musolesi@cl.cam.ac.uk


slide-4
SLIDE 4

mirco.musolesi@cl.cam.ac.uk
 4


Reality
Mining
Dataset


slide-5
SLIDE 5

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


slide-6
SLIDE 6

mirco.musolesi@cl.cam.ac.uk
 6


Credit:
Flutracker.com


slide-7
SLIDE 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


slide-8
SLIDE 8

An
Example
of
Temporal
Graph


A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


8
 mirco.musolesi@cl.cam.ac.uk


slide-9
SLIDE 9

…and
the
Corresponding
Static
Graph


A
 B
 C
 D
 E
 F


9
 mirco.musolesi@cl.cam.ac.uk


slide-10
SLIDE 10

10
 mirco.musolesi@cl.cam.ac.uk


INFOCOM
(2nd
day)


slide-11
SLIDE 11

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


slide-12
SLIDE 12

Calculating
the
Temporal
Distance



A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


12
 mirco.musolesi@cl.cam.ac.uk


slide-13
SLIDE 13

Calculating
the
Temporal
Distance
 (t
=
1)



A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


D
at
distance
1


13
 mirco.musolesi@cl.cam.ac.uk


slide-14
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


14
 mirco.musolesi@cl.cam.ac.uk


slide-15
SLIDE 15

Calculating
the
Temporal
Distance

 
(t
=
3)


A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


B
and
C
at
distance
3


15
 mirco.musolesi@cl.cam.ac.uk


slide-16
SLIDE 16

Calculating
the
Temporal
Distance

 
(t
=
4)


A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


F
at
distance
4


16
 mirco.musolesi@cl.cam.ac.uk


slide-17
SLIDE 17

What
about
the
Static
Distance?


A
 B
 C
 D
 E
 F


17
 mirco.musolesi@cl.cam.ac.uk


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
 A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F
 E
 F
 E
 F
 E
 F


slide-18
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


18
 mirco.musolesi@cl.cam.ac.uk


slide-19
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


19
 mirco.musolesi@cl.cam.ac.uk


slide-20
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


20
 mirco.musolesi@cl.cam.ac.uk


slide-21
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


21
 mirco.musolesi@cl.cam.ac.uk


slide-22
SLIDE 22

Calculating
the
Inverse
Temporal
Distance
 (t
=
4)


A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


22
 mirco.musolesi@cl.cam.ac.uk


A
is
not
reachable
 
[infinite
distance]


slide-23
SLIDE 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


23
 mirco.musolesi@cl.cam.ac.uk


slide-24
SLIDE 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


24
 mirco.musolesi@cl.cam.ac.uk


slide-25
SLIDE 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


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


25
 mirco.musolesi@cl.cam.ac.uk


slide-26
SLIDE 26

Impact
of
the
Horizon
Parameter
 (F
‐>
A,
h
=
2)


A
 B
 A
 B
 A
 B
 A
 B
 C
 D
 C
 D
 C
 D
 C
 D
 E
 F


t
=
1
 t
=
2
 t
=
3
 t
=
4


E
 F
 E
 F
 E
 F


26
 mirco.musolesi@cl.cam.ac.uk


A
was
not
reachable
at
all
with
h
=
1
(in
4
time
windows),
but
with
h
=
2
it
is
a
distance
1!


slide-27
SLIDE 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


27
 mirco.musolesi@cl.cam.ac.uk


slide-28
SLIDE 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


28
 mirco.musolesi@cl.cam.ac.uk


slide-29
SLIDE 29

Local
Temporal
Efficiency


mirco.musolesi@cl.cam.ac.uk
 29


A
 B
 C
 D
 E
 F


Node
i


slide-30
SLIDE 30

Temporal
Clustering
Coefficient


mirco.musolesi@cl.cam.ac.uk
 30


A
 B
 C
 D
 E
 F


Node
i


slide-31
SLIDE 31

INFOCOM
Dataset:
 Static
vs
Temporal
Metrics


H=wfwf


hmin
=
12am,
hmax
=
12pm,
w
=
5
min


mirco.musolesi@cl.cam.ac.uk
 31


Static
metrics
underestimate
L


slide-32
SLIDE 32

Reality
Mining
Dataset


h
=
1,
tmin
=12
am,
tmax
=
12pm,
w
=
5
min


h
=
1,
tmin
=12
am,
tmax
=
12pm,
w
=
5
min


mirco.musolesi@cl.cam.ac.uk
 32


slide-33
SLIDE 33

Variation
of
the
Clustering
Coefficient


  • ver
Time


Reality
Mining
Dataset
(tmin
=
12
am,
tmax
=
12
pm,
w
=
5
min)


mirco.musolesi@cl.cam.ac.uk
 33


slide-34
SLIDE 34

Temporal
Efficiency
vs
Static
Efficiency


mirco.musolesi@cl.cam.ac.uk
 34


MIT
Dataset


slide-35
SLIDE 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


35
 mirco.musolesi@cl.cam.ac.uk


slide-36
SLIDE 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


slide-37
SLIDE 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


37
 mirco.musolesi@cl.cam.ac.uk


slide-38
SLIDE 38

INFOCOM
Dataset:


What
Happens
if
We
Reshuffle
the
Sequence?


h
=
1,
tmin
=12
am,
tmax
=
12pm,
no
runs
=
50


mirco.musolesi@cl.cam.ac.uk
 38


slide-39
SLIDE 39

Email
Dataset


  • Ff


h
=
1,
tmin
=12
am,
tmax
=
12pm,
w
=
5
min


mirco.musolesi@cl.cam.ac.uk
 39