Network Dynamics & Simulation Science Laboratory
Where:
LLNL,
Livermore,

Dates:
December
1st
to
December
15th

2010

Hosts:
Dr.
David
Brown
and
Dr.
Celeste
Matarazzo

Time:
10.00
am
to
11.30
am
(OfMice
hours
as
needed
afterwards)

Lecturer:
Madhav
Marathe,
Virginia
Tech
(mmarathe@vbi.vt.edu)

Guest
Lectures:
Christopher
Kuhlman
(VT),
Goran
Konjevod

(Staff
Scientist,
LLNL),
Anil
Vullikanti
(Asst
Prof.
VT
and
DOE

Career
award
recipient)

Complex
Networks
are
pervasive
in
our
society.
Realistic
biological,
information,
social
and
technical
networks

share
a
number
of
unique
features
that
distinguish
them
from
physical
networks.
Examples
of
such
features

include:
irregularity,
time-‐varying
structure,
heterogeneity
among
individual
components,
and
selMish/
cooperative
game-‐like
behavior
by
individual
components
and
co-‐evolution.
The
size
and
heterogeneity
of
these

networks,
their
co-‐evolving
nature
and
the
technical
difMiculties
in
applying
dimension
reduction
techniques

commonly
used
to
analyze
physical
systems
makes
reasoning,
prediction
and
controlling
of
these
networks
even

more
challenging.

Recent
quantitative
changes
in
high
performance
and
pervasive
computing
including
faster
machines,

distributed
sensors
and
service-‐oriented
software
have
created
new
opportunities
for
collecting,
integrating,

analyzing
and
accessing
information
related
to
such
large
complex
networks.
The
advances
in
network
and

information
science
that
build
on
this
new
capability
provide
entirely
new
ways
for
reasoning
and
controlling

these
networks.
Together,
they
enhance
our
ability
to
formulate,
analyze
and
realize
novel
public
policies

pertaining
to
these
complex
networks.

The
course
will
cover
the
mathematical
and
computational
aspects
of
Network
Science.
It
will
provide
a
broad

overview
of
the
area
and
then
will
focus
on

• Mathematical
aspects,
including
structure
theorems,
existence
proofs,

• Computational
aspects,
including,
provable
lower
as
well
as
upper
bounds
on
the
computational
resources,

efMicient
algorithms
for
computing
the
structure
and
dynamics
over
complex
networks,

• Developing
high
performance
computing
based
computational
models
and
modeling
environments
for

supporting
Network
Science.

Practical
applications
arising
in
the
context
of
infrastructure
planning,
energy
systems,
national
security
and

integrated
communication
systems
will
be
used
to
illustrate
the
applicability
of
the
concepts.

Course Synopsis

Work
funded
in
part
by
NIGMS,
NIH
MIDAS

program,

CDC,
Center
of

Excellence
in
Medical
Informatics,
DTRA
CNIMS,
NSF,
NeTs,

NECO
and
OCI

program,
VT
Foundation.

• 
Lada
Adamic:
For
graciously
sharing
her
course
notes

• 
NDSSL
Laboratory
members
who
are
in
reality
coauthors
of
this.

• 
Other
places
that
I
have
borrowed
the
material
includes:

• Tim
Roughgarden’s
lectures
on
Games

• David
Kempe’s
Lectures
on
Networks

• Henning

Mortveit’s
lectures
on
SDS

• Bogdan
Oporowski’s
lecture
on
Graph
theory

• Michael
Kearns
lectures
on
Networks
and
Games

• …
and
many
more

• Books

• Fernando
Vega-‐Redondo,
Complex
Social
Networks,
Econometric
Society

Monographs,
,

Cambridge
University
Press,
2007

• D.
Easley,
J.
Kleinberg.
Networks,
Crowds,
and
Markets:
reasoning
about
a
Highly

Connected
World,
Cambridge
University
Press,
2010.

• J.
Kleinberg,
E.
Tardos.
Algorithm
Design.
Addison
Wesley,
2005.

Matthew
Jackson,
Social
and
Economic
Networks,
Princeton
University
Press,

2010

• …
and
many
more

Acknowledgements for Course Material

What
is
a
Network?

History,
Broad
Research
Questions,
Illustrative

Applications

What
is
a
network
?

  Although
no
formal
accepted

deMinition,
there
appears
to
be
a

consensus
that
all
network

comprise
of
the
following

attributes:

  A
set
of
agents
(entities):
agents

can
be
simple,
game
like,
adaptive

…

  Interaction
among
the
entities

governed
by
a
graph
(binary
or
in

general
k-‐ary
relationship)

  Graph
itself
can
change,
co-‐evolve
with

the
entities

  Entities
modify
their
local
states

and
behavior
by
interacting
with

their
neighbors

Blogosphere
(datamining.typepad.com)
points lines
vertices edges, arcs math
nodes links computer science
sites bonds physics
actors ties, relations sociology
node
edge

Images
of
Various
Networks

Social
Networks:
Facebook
has
over
500Million

individuals!

http://www.smrfoundation.org/category/industry/companies/facebook/

High
School
Dating
Network
(Discovery
Magazine

2007)

Router-level
network
based
on
ISPs

Delta
Airlines
Routes
(airline
routes
maps.com

EU
rail
network

Biological
Networks

Institute of biology and technology - Saclay (iBiTec-S)/ Unités/
Department of Integrative Biology and Molecular Genetics (SBiGeM)/
Integrative biology laboratory (LBI)/ Dynamics of Biological Network (J. Labarre)
http://djpowell.wordpress.com/
http://www.leonelmoura.com/tree.html

In
real
world
Networks
are
layered
and

coupled

Growth
of
network
science
as
measured
by

publications

#papers
with
“complex
networks”

in
the
title

[National
Academy
of
Science

Report,
2007]

Journal
special
issues
on
Network

Science

Even
appears
in
main
stream
publications

YESTERDAY
!

The
Emerging
Network
Science?

  Newman,
Barabasi,
Watts:
The
Structure
and
Dynamics
of
Networks:
“We

argue
that
the
science
of
networks
that
has
been
taking
shape
over
the
last
few

years
is
distinguished
from
preceding
work
on
networks
in
three
important

ways:

  (1)
by
focusing
on
the
properties
of
real-‐world
networks,
it
is
concerned
with

empirical
as
well
as
theoretical
questions;

  (2)
it
frequently
takes
the
view
that
networks
are
not
static,
but
evolve
in
time

according
to
various
dynamical
rules;
and

  (3)
it
aims,
ultimately
at
least,
to
understand
networks
not
just
as
topological

objects,
but
also
as
the
framework
upon
which
distributed
dynamical
systems
are

built.”

  Kearns:
An
Emerging
Science:

  Examine
apparent
similarities
(and
differences)
between
many
social,

economic,
information,
biological
and
technological
networks

  Importance
of
network
effects
in
such
systems

  How
things
are
connected
matters
greatly

  Details
of
interaction
matter
greatly

  Qualitative
and
quantitative;
can
be
very
subtle

  A
revolution
of
measurement,
theory,
and
breadth
of
vision

Science
of
Networks:
A
personal
(and
likely

biased)
viewpoint
1:

  Real
World
Networks:

  Extremely
important
but
..

  Folks
in
social
sciences,
transportation,
electrical
systems,
VLSI,
…
all

have
been
studying
real
world
networks

  We
need
to
seriously
revisit
the
use
of
simple
random
graph
models
as

a
way
to
explain
a
phenomenon:
the
mathematics
is
elegant
but
often

means
very
little
in
the
real
world

  Real
world
networks
are
dynamic,
coupled
and
co-‐evolve

  Ability
to
collect
data
that
is
diverse
(spatially,

demographically),
process
it,
store
it
and
reason
about
it
very

fast

  New
data
should
be
utilized
in
developing
network
models

New
and
realistic
models
of
real
world
networks.

Models
should
represent
coupling
and
co-evolution

Accessibility
of
Network
Science:
Pervasive
Computing

Environment

  High
performance
computing
(larger
machines,
data
intensive
systems,

distributed
systems
…)

  Software
as
a
service;
delivering
results
to
specialist
who
is
not

interested
in
becoming
a
computer
scientist

  Ability
to
collect
data
that
is
diverse
(spatially,
demographically),
process

it,
store
it
and
reason
about
it
very
fast

Develop
Pervasive
computing
technology
to
deliver

Network
Science
technology
to
domain
specialists
and

others
who
are
not
computing
experts

Science
of
Networks:
Centrality
of
Computing
and

Information
Science

  From
analytical
results
to
algorithmic
viewpoint:
this
is
the
essence
of

new
science
in
my
opinion
if
one
has
to
do
deal
with
real
networks

  Questions
that
become
important
are:

  How
can
we
design
certain
networks

  How
can
we
measure
distributed
networks

  What
is
a
certain
set
of
distributed
agents
computing:
interaction
based
computing
and

social
cognition

  Models
are
not
monolithic
or
federated
anymore
but
really
a
way
to

synthesize
information
by
interacting
with
various
components
–

Milner’s
in_luential
idea
on
interactionism

Algorithmic
Viewpoint

provide
the
foundational
basis

HPC
computing
provide
the
underlying
technology

Inter
and
intra-discipline
interactions
–

Emergence
of
a
Giant
Component
!

  We
have
reached

critical
point
wherein
researchers
from
diverse

disciplines
are
starting
to
share
their
ideas
and
interact

(Gladwell’s
Tipping
point)

  Beautiful
convergence
of
ideas
and
view
points
in
CS,
Engineering,

Economics,
Mathematics,
Physics,

Social
Science,
Biology….

(convergence
of
several
events,
world
becoming
smaller,
funding

agencies
pushing
to
do
joint
work!,
global
problems,
problems
that

were
being
solved
by
disciplinary
viewpoints)

  Economic
drivers:
Information
economy,
distributed
logisitics,

global
markets,
mobile
labor
force,
funding
shortfalls

  Measurement
technologies
and
technologies
for
developing
and

sustaining
diverse
organizations
and
ecosystems
have
taken
hold

Multi-disciplinary
view
important:
from
real
research

social
networks
!

Culmination
of
diverse
_ields:
Viewpoints

are
different
and
interesting

Engineers

• Understand
how
infrastructure

networks
work

• Design
and
control
of
these

networks

Computer
Scientists

• Understand
and
design
complex,

distributed
networks

• 
algorithmic
view:

design
of
a

system
and
inferring
its

semantics

Social
Scientists,
Behavioral

Psychologists,
Economists

• Understand
human
behavior
in

“simple”
settings

• Revised
views
of
economic

rationality
in
humans

Biologists

• Neural
networks,
gene
regulatory

networks,…

• Understanding
the
evolution
of

networks

Physicists
and

Mathematicians

• Interest
and
methods
in
complex

systems

• Theories
of
macroscopic
behavior

(phase
transitions)

Scientists forming
co-evolving
networks World

Proposed
Components
of
a
Research
Program
in

Network
Science
and
Engineering

Structural
Analysis

of
Complex

Networks

Dynamics
on

Complex
Networks

Co-‐evolution
of

dynamics,
network

and
individual

behavior

Measurement
and

Inference

Networks
Science in Real
World

Key
Research
Challenges
(NA
report
on
Network

Science)

1.  Dynamics:
Better
understanding
between
structure

and
function

2.  Modeling
and
Analysis
of
large
networks:
Tools,

abstractions,
approximations

3.  Design
and
Synthesis
of
Networks

4.  Increasing
level
of
rigor
and
mathematical
structure

5.  Abstracting
common
concepts
across
Mields

6.  Better
experiments
and
measurements
of
network

structure

7.  Robustness
and
Security

Motivating
examples/applications

Application
1
(1736):
First
Use
of
Graphs

Seven
Bridges
of
Königsberg

  Seven
Bridges
of
Königsberg
–
one
of
the
Mirst
problems
in
graph

theory

  Is
there
a
route
that
crosses
each
bridge
only
once
and
returns
to
the

starting
point?

We
will
see
how
this
problem
can
be
solved
by
modeling
it
as
a

graph
theory
problem
later

Application
2
(1850s):

Cholera
Pandemic:
John
Snow

First
Cholera
Pandemic

Second
Cholera
Pandemic

 During
this
time
germ
theory
of
diseases
was

not
widely
accepted.

 During
John
Snow's
life
time
there
were
three

pandemics
of
Asiatic
cholera
(1817-‐23,
1826-‐37

and
1846-‐63),
two
of
which
reached
the
British

isles.

 
The
epidemic
in
1848
to
1849,
killed

between

50,000
and
70,000
in
England
and
Wales.
A
third

outbreak
in
1854
left
over
30,000
people
dead
in

London
alone.

 Vibrio
cholerae:
Toxin
alters
sodium
pump
in

intestinal
cells

Mluid
loss

 Entry:
oral
Colonization:
small
intestine

Symptoms:
nausea,
diarrhea,
muscle
cramps,

shock

http://www.ph.ucla.edu/epi/snow.html

Application
3
(1950-60)

Segregation
(Schelling):
Micromotives
to
Macrobehavior

  Duncan
and
Duncan’s
(1957)
study
of
Chicago

  1940-‐1950
Census
tracts,
mixed
neighborhoods
all
segregate

  Placed
pennies
and
dimes
on
a
chess
board
and
moved
them

around
according
to
various
rules.

  Board
=

city,

Square
=
Housing
lot,
agent:
at
a
location

  Pennies
and
dimes
=
agents
representing
two
groups
in
society,

e.g.
boys
and
girls,
smokers
and
non-‐smokers,
etc.

  Neighborhood
=adjacent

locations
on
the
board

  Happy
if
(neighbors
of
same
type
>
threshold)

  If
Unhappy
then
move
to
a
random
location

that
is
happy

  Result:
Many
basic
conMigurations
produce
segregation

  relate
decisions
about
where
to
live
(micro)
to
patterns
of

segregation
(macro)

  No
obvious
relationship
between
individual
behavior
and

aggregate
outcomes.

  Behavior
is
interdependent.
Individuals’
behaviors
depend
on

social
context
(micro)

  Individual
behaviors
collectively
change
social
context
(long

term,
macro)

http://cs.gmu.edu/~eclab/projects/mason/projects/schelling/

Application
4:
Power
grids
and
cascading
failures

  Vast
system
of
electricity
generation,
transmission
&
distribution
is

essentially

a
single
network

  Power
Mlows
through

all
paths
from
source
to
sink

(Mlow
calculations
are

important
for
other
networks,

even
social
ones)

  All
AC
lines
within
an

interconnect
must
be
in
sync

  If
frequency
varies
too
much
(as
line
approaches
capacity),
a
circuit

breaker
takes
the
generator
out
of
the
system

  Larger
Mlows
are
sent
to
neighboring
parts
of
the
grid
–
triggering
a

cascading
failure

Application
4:

Blackout
of
2003:

  Electrical
Infrastructure

Affected

  Area
of
50
million
people
in
eight
US

states
and
two
provinces
in
Canada

  Approximately61,800Megawatts
(MW)oMload

  Most
cascaded
happen
extremely

rapidly
from
4.10
pm
to
4.13
pm

  Human
and
information
system

error
also
contributed
to
the

cascade

  Other
Infrastructures
including

water,
communication,
and
most

notably
transportation
(rail,
road

and
air)
were
affected

  TV
and
radio
stations
also

affected

Timeline
for
2003
Blackout:
Need
for
Multi-level

networks

The
2003
blackout
wasn't
just
about
fallen
trees
and
broken

transmission
lines.
As
this
timeline
from
the
Department
of
Energy

report
shows,
it
resulted
from
a
combination
of
many
grid
events,

computer
glitches,
and
human
interaction.

Blackout
of
2003:Time
Line
–
The
Initial
Phase

  12:15
p.m.
Incorrect
telemetry
data
renders
inoperative
the
state
estimator,
a
power
Mlow

monitoring
tool
operated
by
the
Indiana-‐based
Midwest
Independent
Transmission
System
Operator
(MISO).
An
operator
corrects
the
telemetry

problem
but
forgets
to
restart
the
monitoring
tool.

  1:31
p.m.
The
Eastlake,
Ohio
generating
plant
shuts
down.
The
plant
is
owned
by
FirstEnergy,
an

Akron,
Ohio-‐based
company
that
had
experienced
extensive
recent
maintenance
problems.

  2:02
p.m.
The
Mirst
of
several
345
kV
overhead
transmission
lines
in
northeast
Ohio
fails
due
to

contact
with
a
tree
in
Walton
Hills,
Ohio.

 
2:14
p.m.
An
alarm
system
fails
at
FirstEnergy's
control
room
and
is
not
repaired.

  3:05
p.m.
A
345
kV
transmission
line
known
as
the
Chamberlain-‐Harding
line
fails
in
Parma,
south

of
Cleveland,
due
to
a
tree.

  3:17
p.m.
Voltage
dips
temporarily
on
the
Ohio
portion
of
the
grid.
Controllers
take
no
action.

  3:32
p.m.
Power
shifted
by
the
Mirst
failure
onto
another
345
kV
power
line,
the
Hanna-‐Juniper

interconnection,
causes
it
to
sag
into
a
tree,
bringing
it
ofMline
as
well.
While
MISO
and
FirstEnergy

controllers
concentrate
on
understanding
the
failures,
they
fail
to
inform
system
controllers
in

nearby
states.

  3:39
p.m.
A
FirstEnergy
138
kV
line
fails
in
northern
Ohio.

  3:41
p.m.
A
circuit
breaker
connecting
FirstEnergy's
grid
with
that
of
American
Electric
Power
is

tripped
as
a
345
kV
power
line
(Star-‐South
Canton
interconnection)
and
Mifteen
138
kV
lines
fail
in

rapid
succession
in
northern
Ohio.

http://en.wikipedia.org/wiki/Northeast_Blackout_of_2003

Blackout
of
2003:
Timeline
--

the

cascade
begins

  3:46
p.m.
A
Mifth
345
kV
line,
the
Tidd-‐Canton
Central
line,
trips
ofMline.

  4:05:57
p.m.
The
Sammis-‐Star
345
kV
line
trips
due
to
undervoltage
and
overcurrent

interpreted
as
a
short
circuit.
Later
analysis
suggests
that
the
blackout
could
have
been

averted
prior
to
this
failure
by
cutting
1.5
GW
of
load
in
the
Cleveland–Akron
area.

  4:06–4:08
p.m.
Sustained
power
surge
north
toward
Cleveland
overloads
3
138
kV
lines.

  4:09:02
p.m.
Voltage
sags
deeply
as
Ohio
draws
2
GW
of
power
from
Michigan,
creating

simultaneous
undervoltage
and
overcurrent
conditions
as
power
attempts
to
Mlow
in
such
a

way
as
to
rebalance
the
system's
voltage.

  4:10:34
p.m.
Many
transmission
lines
trip
out,
Mirst
in
Michigan
and
then
in
Ohio,
blocking
the

eastward
Mlow
of
power
around
the
south
shore
of
Lake
Erie.
Suddenly
bereft
of
demand,

generating
stations
go
ofMline,
creating
a
huge
power
deMicit.
In
seconds,
power
surges
in
from

the
east,
overloading
east-‐coast
power
plants
whose
generators
go
ofMline
as
a
protective

measure,
and
the
blackout
is
on.

  4:10:37
p.m.
The
eastern
and
western
Michigan
power
grids
disconnect
from
each
other.
Two

345
kV
lines
in
Michigan
trip.
A
line
that
runs
from
Grand
Ledge
to
Ann
Arbor
known
as
the

Oneida-‐Majestic
interconnection
trips.
A
short
time
later,
a
line
running
from
Bay
City
south

to
Flint
in
Consumers
Energy's
system
known
as
the
Hampton-‐Thetford
line
also
trips.

  4:10:38
p.m.
Cleveland
separates
from
the
Pennsylvania
grid.

Blackout
of
2003:
Timeline
--
Crescendo

  4:10:39
p.m.
3.7
GW
power
Mlows
from
the
east
along
the
north
shore
of
Lake
Erie,
through

Ontario
to
southern
Michigan
and
northern
Ohio,
a
Mlow
more
than
ten
times
greater
than
the

condition
30
seconds
earlier,
causing
a
voltage
drop
across
the
system.
4:10:40
p.m.
Flow
Mlips
to

2
GW
eastward
from
Michigan
through
Ontario
(a
net
reversal
of
5.7
GW
of
power),
then
reverses

back
westward
again
within
a
half
second.

  4:10:40
p.m.
Flow
Mlips
to
2
GW
eastward
from
Michigan
through
Ontario
(a
net
reversal
of
5.7

GW
of
power),
then
reverses
back
westward
again
within
a
half
second.

  4:10:43
p.m.
International
connections
between
the
United
States
and
Canada
begin
failing.

  4:10:45
p.m.
Northwestern
Ontario
separates
from
the
east
when
the
Wawa-‐Marathon
230
kV

line
north
of
Lake
Superior
disconnects.
The
Mirst
Ontario
power
plants
go
ofMline
in
response
to

the
unstable
voltage
and
current
demand
on
the
system.

  4:10:46
p.m.
New
York
separates
from
the
New
England
grid.

  4:10:50
p.m.
Ontario
separates
from
the
western
New
York
grid.

  4:11:57
p.m.
The
Keith-‐Waterman,
Bunce
Creek-‐Scott
230
kV
lines
and
the
St.
Clair-‐Lambton
#1

230
kV
line
and
#2
345
kV
line
between
Michigan
and
Ontario
fail.

  4:12:03
p.m.
Windsor,
Ontario
and
surrounding
areas
drop
off
the
grid.

  4:12:58
p.m.
Northern
New
Jersey
separates
its
power-‐grids
from
New
York
and
the
Philadelphia

area,
causing
a
cascade
of
failing
secondary
generator
plants
along
the
Jersey
coast
and

throughout
the
inland
west.

  4:13
p.m.
End
of
cascading
failure.
256
power
plants
are
off-‐line,
85%
of
which
went
ofMline
after

the
grid
separations
occurred,
most
due
to
the
action
of
automatic
protective
controls.

Milgram’s
Small
World
Experiment

  Travers
&
Milgram
1969:
classic
early
social

network
study

  destination:
a
Boston
stockbroker;

lived
in
Sharon,
MA

  sources:
Nebraska
stockowners;

  forward
letter
to
a
Mirst-‐name

acquaintance
“closer”
to
target

  Information
provided:

  name,
address,
occupation,
Mirm,
college,
wife’s

name
and
hometown

  navigational
value?

  Basic
Mindings:

  64
of
296
chains
reached
the
target

  20%
of
senders
reached
target.

  average
chain
length
=
6.5:
“Six
degrees
of
separation”

  average
length
of
completed
chains:
5.2

  interaction
of
chain
length
and
navigational

difMiculties

  main
approach
routes:
home
(6.1)
and
work

(4.6)

  Boston
sources
(4.4)
faster
than
Nebraska
(5.5)

  no
advantage
for
Nebraska
stockowners

NE
MA

Recent
small
world
experiment

Setup

  Email
experiment

Dodds,

Muhamad,
Watts,

Science
301,

(2003)

  18
targets,
13
different
countries

60,000+
participants

  a
professor
at
an
Ivy
League

university,

  an
archival
inspector
in
Estonia,

  a
technology
consultant
in
India,

  a
policeman
in
Australia,

  a
veterinarian
in
the
Norwegian

army.

Basic
Analysis

  Approximate
37%
participation
rate

approximately
.

  Probability
of
a
chain
of
length
10

getting
through:

  .3710
~
5
x
10-‐5

  so
only
one
out
of
20,000
chains
would

make
it

  actual
#
of
completed
chains:
384

(1.6%
of
all
chains).

  Average
path
length:
4,
median:
7

  Small
changes
in
attrition
rates
lead
to

large
changes
in
completion
rates

  e.g.,
a
15%
decrease
in
attrition
rate

would
lead
to
a
800%
increase
in

completion
rate

Estimating
‘recovered’
chain
lengths
for
uncompleted

chains

  <L>
=
4.05
for
all
completed
chains

  L*
=
Estimated
`true'
median
chain
length

  Intra-‐country
chains:
L*
=
5

  Inter-‐country
chains:
L*
=
7

  All
chains:
L*
=
7

  Milgram:
L
*
~
8-‐9
hops

Attrition
rate
stays
approx.
constant
throughout

  rL
–
probability
of
not
passing
on
the
message
at

distance
L
from
the
source

average
95 % confidence interval

Estimated
‘recovered’
chain
lengths

  observed
chain

lengths

  ‘recovered’

histogram
of

path
lengths

 

inter-‐country

intra-‐country

Small
world
experiment
at
Columbia

 Successful
chains
disproportionately
used

 
weak
ties
(Granovetter)

 
professional
ties
(34%
vs.
13%)

 
ties
originating
at
work/college

 
target's
work
(65%
vs.
40%)

 .
.
.
and
disproportionately
avoided

 
hubs
(8%
vs.
1%)
(+
no
evidence
of
funnels)

 
family/friendship
ties
(60%
vs.
83%)

 Strategy:
Geography
-‐>
Work

How
many
hops
actually
separate
any
two
individuals

in
the
world?

  Participants
are
not
perfect
in
routing
messages

  They
use
only
local
information

  “The
accuracy
of
small
world
chains
in
social
networks”

Peter
D.
Killworth,
Chris
McCarty
,
H.
Russell
Bernard&
Mark
House:

  Analyze
10920
shortest
path
connections
between
105

members
of
an
interviewing
bureau,

  together
with
the
equivalent
conceptual,
or
‘small
world’
routes,

which
use
individuals’
selections
of
intermediaries.

  This
permits
the
Mirst
study
of
the
impact
of
accuracy
within

small
world
chains.

  The
mean
small
world
path
length
(3.23)
is
40%
longer
than
the

mean
of
the
actual
shortest
paths
(2.30)

  Model
suggests
that
people
make
a
less
than
optimal
small

world
choice
more
than
half
the
time.

Tentative
Schedule

  Week
1
–
Module
1.
December
1-‐2
(Wednesday,
&
Thursday)

  Wednesday(1st
December):
Introduction
to
Network
Science

  Thursday(2nd
December):
SDS
and
Diffusion
on
Networks,

  Friday
(Extra
Class
if
interest):
EpiCure
–
modeling
environment
for
studying

malware
propagation
in
wireless
networks.

 
Week
2
–
Module
2
December
7-‐9

(Monday,
Tuesday,
Thursday)

  Monday
(6th
December):

Control
and
InMluence
maximization

  Tuesday
(7th
December):
Branching
process
result,
proof
of
Fastdiffuse.
Introduction
to

various
diffusion
style
modeling
environments

  Wednesday
(Extra
class
if
interest):

Population
and
Network
Synthesis.
Introduction

to
graph
analysis

  Thursday
(9th
December):
SIMDEMICS
and
related
modeling
environments.

  Week
3
–
Module
3
and
Module
4
(December
13-‐16)

  Monday
(13th
December):
Markets,
Games,
Mechanism
Design
and
SIGMA:
a
modeling

environment
to
study
commodity
markets
on
networks,

  Tuesday
(14th
December):
Shortest
Paths,
Formal
language
constrained
paths,
Greedy

routing,
routing
in
small
world
networks,
Introduction
to
TRANSIMS.

  Thursday
(15th
December):

Concluding
remarks,
Brief
discussion
of

uncovered
topics,

Open
Problems,
Directions
for
Future
Work.

Network Science: Theory, Modeling and Applications