possibility networks

“Possibility Networks”An Exploration of Complex Network Theory and

Its Potential Uses for Futures

For the Association of Professional Futurists Professional Development Seminar

Chicago, IllinoisJuly 29th, 2005

By: David A. Jarvis

2

An Opening Thought…

“The greatest challenge today, not just in cell biology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down many

kinds of systems. They think they know most of the elements and forces. The next task is to

reassemble them, at least in mathematical models that capture the key properties of the entire

ensembles.”

- E.O. Wilson, Consilience: The Unity of Knowledge

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Why Complex Networks and Futures?

• It has been expressed by members of the APF that the futures field needs new tools, techniques and methodologies – The field’s last major development was scenario planning, which

evolved from military planning during World War II and was adopted by the corporate world in the 1960’s

– In a recent APF professional development survey, members said they wanted more information on simulation and games, chaos and agent-based models

• Complex systems can significantly augment the spectrum of tools that futurists can offer clients and organizations

• Those trained in studying the future have explored systems thinking, chaos and complex systems, but tools and applications have not widely moved beyond the metaphorical level

• Where do complex systems and the systemic study of the future intersect? Can new tools be created for futurists extracted from the research done in complex systems?

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What to Expect

• Gain a basic understanding of the science and math behind network theory - what it is and what it isn’t

• Learn about the major players in network theory and the foundational books and papers for the field

• Understand the theoretical basis behind such concepts as “diffusion of innovations” and “idea contagions”

• Learn how social networks can be used as a futures tool

• Participate in an exercise demonstrating the usefulness and power of social networks

• This is a BROAD and SHALLOW view of network theory – its purpose is to stimulate thinking and help form questions

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Introduction

I. History and Background

II. Scientific Basics

III. Examples and Applications

IV. Demonstration

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Definition of a Complex Network

• A society tends to view itself through a lens of the technologies it creates

• Networks are EVERYWHERE!– Power grids– Computer networks– Ecological systems (e.g. food webs)– Social interaction patterns– Romantic and sexual networks– The Internet and World Wide Web– Transportation (roads, airlines, rail, etc.)– Communication networks (phones, post, etc.)– Protein interactions and cellular networks– Biological systems (the brain, circulatory system, etc.)

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• Complex system - a collection of interacting elements arranged for purpose that exhibits high-dimensionality, non-linearity, sensitive dependence of initial conditions, and possibly emergent behavior

• Complex network - a representation of a complex system, comprised of nodes and links

Definition of a Complex Network

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I. History and Background

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The Seven Bridges of Königsberg

• Question: Is it possible to cross all seven bridges only once and return to your starting point?

• In 1736, Leonhard Euler proved that it was not possible through one of the first formal mathematical discussions using graph theory

Node

Link

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Paul Erdős

• Hungarian mathematician and prolific scientific author

• With Alfréd Rényi did fundamental research into how networks form

• Discovered random network theory – simplest method of creating a network, God plays dice

• Emergence of a giant component• Erdős number – small world

phenomenon

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Buttons and Strings

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The Strength of Weak Ties

• Mathematical sociologist Mark Granovetter (article in American Journal of Sociology, 1973)

• “…the degree of overlap of two individuals’ friendship networks varies directly with the strength of their tie to one another.”

• Weak ties can serve as bridges between different social groups, allow you to reach more people more quickly

• Strong ties lead to

fragmentation, weak ties lead

to integration• Example: finding a job

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Six Degrees of Separation

• Hungarian author Karinthy’s short story entitled “Chains” (1929)

• Milgram’s experiment (1967)– Find the “distance” between any two people in the U.S.– Sent a letter to a few hundred randomly selected

people from Boston and Omaha with instructions to send to a Massachusetts stockbroker, the recipient could only send the letter to someone they knew on a first name basis

– Common sense says it should take hundreds of steps, it only took six on average, it’s a small world after all!

– Idealized vs. real social networks

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Small Worlds & Scale Free• Small world networks

– Duncan Watts and Steven Strogatz (1998)– Each node can reach every other node in a small number

of steps– Characterized by high clustering, short characteristic path

lengths

• Scale-free networks– Albert-László Barabási (professor of physics at Notre

Dame) & Réka Albert (currently at Penn State)– Examined networks that exhibited a power-law distribution

in their degree (Internet and WWW)• Large number of poorly connected nodes and a small number of

well-connected hubs

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Scale-Free Networks

• Poisson distributions vs. power-law distributions– Power law example: distribution of wealth

Normal (Poisson) Distribution Power-Law Distribution

Number of links (k) Number of links (k)

Nu

mb

er

of

no

de

s w

ith k

lin

ks

Nu

mb

er

of

no

de

s w

ith k

lin

ks Most nodes have the same number of links

Large number of nodes have few links

Small number of nodes (hubs) have many links

Adapted from: Linked, Barabási , pg. 71

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Related Topics

• Fads• Memes • Chaos Theory• Social Networking• Diffusion of Innovations• Contagion• Agent-Based Modeling• Collective Robotics and Distributed Systems• Emergence

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Fads

• Definition – Ideas or things in a culture that become extremely popular very quickly, and just as quickly become unpopular; linked to herd mentality– Bandwagon effect – a benefit that a person enjoys as a result of

others’ doing the same thing that they do

• Relation – accelerated s-curve behavior • Examples

– Irrational exuberance in the stock market– Flash mobs– Christmas toys– Fashion– Music & dance crazes

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Memes

• Definition – concept created by Richard Dawkins in his book The Selfish Gene (1976); a piece of information that can be transmitted between two minds; parallels to evolution

• Relation – Alternate explanation

for how ideas propagate

through a society

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Chaos Theory

• Definition – “The irregular, unpredictable behavior of deterministic, nonlinear dynamical systems.”, Roderick V. Jensen, Yale University

• Relation – descriptive of natural systems, sensitivity to initial conditions, patterns

• Examples– Double pendulums– Multi-body gravitational problems– Turbulent fluids (e.g. the atmosphere)– Work of Lorenz, Mandelbrot

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Diffusion of Innovations• Definition –

– The theories of diffusion can trace their roots back to the French sociologist Gabriel Tarde who identified the innovation adoption S-curve, group mind, laws of imitation

– Progressed through the agricultural research of Ryan and Gross in the 1940’s, lead to the notion of adopter categories (innovators, early adopters, early majority, late majority, laggards)

– Rogers seminal work Diffusion of Innovation (1962) formalized these theories

• Relation – there are many researches who study the diffusion of innovations in complex networks

• Information Flow in Social Groups• A generalized model of social and biological contagion• Modeling diffusion of innovations in a social network• The Power of a Good Idea: Quantitative Modeling of the Spread of

Ideas from Epidemiological Models

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Contagion

VIDEO

“Contact Networks in Predicting and Controlling Emerging Infectious Diseases”

Lauren Ancel Meyers

SFI External Faculty, University of Texas at Austin

7:00 - 15:30 – Background30:00 - 36:00 – Contact Network Epidemiology

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Agent-Based Modeling

• Definition – ABM is a simulation tool that is characterized by large numbers of simple agents interacting through well defined rule sets

• Relation – ABM is widely used as a tool for modeling complex adaptive systems

• Examples– Crowd dynamics– Traffic patterns– Economic markets– Insect behavior – Genetic algorithms

Bonabeau, Eric (2002) Proc. Natl. Acad. Sci. USA 99, 7280-7287

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Emergence• Definition – surprising or unexpected global results that can

occur when the parts of any system interact locally via simple rules; the whole is greater than the sum of its parts

• Relation – Emergent behavior arises in complex systems; self-organization

• Examples– Human consciousness– Traffic patterns– Galaxy formation– Ant colonies, flocking behavior– Urban evolution– Life

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Emergence

“I begin to think that this matter of ‘late emergent properties’ that the physicists talk about when they discuss complexity and cascading sensitivities is an important concept for historians. Justice may be an late emergent property. And maybe we can glimpse the beginnings of it emerging; or maybe it emerged long ago, among the primates and proto-humans,

and is only now gaining leverage in the world, aided by the material possibility of postscarcity.”

- The Years of Rice and Salt, Kim Stanley Robinson

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Social Networking• Definition – business

and social networking services

• Relation – uses complex network principles like “small worlds” and “six degrees of separation”

• Examples– Friendster

– LinkedIn

– Orkut

– Yahoo 360

– MySpace

– Ryze

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Collective Robotics• Definition – large numbers of coordinated simple robots

designed to perform a complex task, inspired by social insects

• Relation – still a very immature technology, collective robotics uses agent-based modeling and principles of emergence

• Examples– Swarms of unmanned military vehicles (air, land, sea)– Mobile sensors networks for ocean research, search and rescue, etc.

Image taken from iRobot website

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Complex Network Literature

• Multi-disciplinary

• Most works are fairly recent

• Still no definitive academic textbook on complex networks

• Three levels– Metaphor– Popular Scientific– Technical

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Metaphor

• The Tipping Point: How Little Things Can Make a Big Difference by Malcolm Gladwell (2000)

• The Rise of the Creative Class: And How It's Transforming Work, Leisure, Community and Everyday Life by Richard Florida (2002)

• The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations by James Surowiecki (2004)

• Smart Mobs: The Next Social Revolution by Howard Rheingold (2003)

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Popular Scientific

• Linked: How Everything Is Connected to Everything Else and What It Means by Albert-Laszlo Barabasi (2002)

• Small Worlds: The Dynamics of Networks between Order and Randomness by Duncan Watts (1999)

• Critical Mass: How One Thing Leads to Another by Philip Ball (2004)• Harnessing Complexity: Organizational Implications of a Scientific

Frontier by Robert Axelrod, Michael D. Cohen (2000)

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Technical

• Adaptation in Natural and Artificial Systems : An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence by John H. Holland (1992)

• Theories of Communication Networks by Peter R. Monge, Noshir S. Contractor (2003)

• Social Network Analysis : Methods and Applications by Stanley Wasserman, Katherine Faust (1995)

• Technical Papers

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VIDEO

“Social Theories of Human Communication Networks” Peter Monge

Professor, Annenberg School for Communication,

University of Southern California

8:20 - 14:10 – Role that networks play in society

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Institutions and Organizations

• Santa Fe Institute• Center for Complex Network Research, University of

Notre Dame• Collective Dynamics Group, Department of Sociology,

Columbia University• Center for the Study of Complex Systems, University of

Michigan• Networks and Social Dynamics at Cornell University• Northwestern Institute on Complex Systems,

Northwestern University• New England Complex Systems Institute (NECSI)• International Network for Social Network Analysis

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Companies

• Marketing– Visible Path

• How to leverage “relationship capital”– Spoke

• Identifying business prospects– Books

• The Anatomy of Buzz, by Emanuel Rosen• Seth Godin’s books (Purple Cow, Unleashing the Ideavirus)• Buzzmarketing, by Mark Hughes

• Icosystems (Cambridge, MA)– Eric Bonabeau

• NuTech Solutions (Charlotte, NC)– Used to be Biosgroup

• Redfish Group (Santa Fe, NM)– Visualization, modeling, simulation and adaptive systems design

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II. Scientific Basics

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Network Theory Basics

• Types of networks• Classes of networks

– Technological– Social– Biological (Ecological)– Information

• Examples• Important network properties• Software applications

36

Types of Networks

• Minimally connected– Network has one less link than the number of nodes, a chain

• Maximally connected– Each node is connected to every other node in the network

• Random – Links are assigned randomly between nodes

• Regular– Each node in the network has an identical degree, a grid

• Small world– A regular network with shortcuts

• Scale-free w/preferential attachment– Degree distribution follows a power-law, as the network grows new

links are more likely to attach to hubs (rich get richer)

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Types of Networks

Minimally connected Maximally connected

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Types of Networks

Erdös random network Random network w/growth

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Types of Networks

Regular network (lattice) Small world network

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Types of Networks

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8

“Scale Free,”Power Law

Scale-free network w/preferential attachment

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Classes of Networks• Technological

– Man-made networks created for the distribution of some resource or commodity

– Electric power grid, airlines, roads, railways, pedestrian traffic, Internet, telephone, post

• Social– Group of people connected by a pattern of interactions– Friendships, business relationships, intermarriages, email,

collaboration– Problems include inaccuracy, subjectivity and small sample size

• Biological– Metabolic pathways, protein interactions, genetic regulatory

networks, food webs, neural networks, blood vessels

• Information– Citation networks (patents, papers), World Wide Web

Source: Newman, M. E. J., The structure and function of complex networks

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THE INTERNET

Technological Networks

Source: Hal Burch and Bill Cheswick, Lumeta Corp

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Technological Networks

AIRLINE ROUTE MAP

Source: Continental Airlines

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ENRON EMAIL DATA

Social Networks

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Social Networks

HIGH SCHOOL DATING

Source: Image by Mark Newman, data drawn from Peter S. Bearman, James Moody, and Katherine Stovel, Chains of affection: The structure of adolescent romantic and sexual networks, American Journal of Sociology 110, 44-91 (2004).

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Biological Networks

FOOD WEBSource: Freshwater food web: Neo Martinez and Richard Williams

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Information Networks

2004 Election “Blogosphere” Source: HP Labs

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• Network Considerations– Structure: The definition of links, nodes and

their possible connections– Dynamics: Feed-back or feed-forward links

that create network effects– Evolution: Long-term statistics as the network

fulfills its purpose

Important Network Properties

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Important Network Properties• Number of nodes and links• Link/node ratio

– helpful in comparing the structural similarity of networks with different sizes• Degree distribution

– a representation of the connection pattern of a network; how many nodes have a specific degree

• Characteristic path length (CPL) – the median of the average distance from each node to every other node in the

network– useful in measuring diffusion rates in the network

• Clustering– a measure of local cohesion in a network– measures the extent to which nodes that are connected to a particular node are also

connected to each other • Susceptibility/Resilience/Robustness

– the extent a network can avoid catastrophic failure as links or nodes are removed and how other properties are affected by node/link removal

• Betweenness– measure of a node’s importance to dynamic behaviors in a complex network– measures the extent to which a node serves as an intermediary between other nodes– number of shortest paths that pass through a node

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Characteristic path length (CPL)

CPL = 1.5 (median of the averages)

0

1

1

2

1

1

F

1.2

1.4

1.8

2.0

1.2

1.6

Avg

11211F

01212E

10322D

23012C

12101B

22210A

EDCBA

D

Link/node ratio = 1.33 (8 links, 6 nodes)


Degree distribution (histogram)

0

1

2

3

1 2 3 4 5 6 7 8

# of connections per node

# o

f n

od

es

Nodes

LinksA

B

C

E

F

2

3

42

4

1Degree

51

A

B

C D

E

F

Clustering coefficient

C = 3 x 3 / 34 = ~0.26

nodes of triplesconnected ofNumber

trianglesof #x 3C

Betweenness - Can be used as a measure of network resilience

ikjng

kjg

inC

g

ngnC

ijk

jk

iB

kj jk

ijkiB

contain that and actors linking )(geodesics pathsshortest of # )(

and actors two thelinking )(geodesics pathsshortest of #

nodefor centrality ss Betweenne)(

)()(


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Source: Newman, M. E. J., Random graphs as models of networks

You can destroy the giant component of a power-law graph

by removing less than 3% of high-degree nodes

The most robust graphs have an α of around 2.2

Robustness - What fraction of nodes need to be removed to destroy the giant component in a power-law graph?

)(1

)(

ck

c

Hf


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Selected Scale-Free Networks

Source: Newman, M. E. J., The structure and function of complex networks

Network Type n l z d α C(1) C(2) r

SocialE-mail messages

Directed 59,912 86,300 1.44 4.95 1.5/2.0

0.16

SocialFilm actors

Directed 449,913 25,516,482 113.43 3.48 2.3 0.20 0.78 0.208

InformationWWW nd.edu

Directed 269,504 1,497,135 5.55 11.27 2.1/2.4

0.11 0.29 -0.067

BiologicalProtein interactions

Undirected 2,115 2,240 2.12 6.80 2.4 0.072 0.071 -0.156

BiologicalMetabolic network

Undirected 765 3,686 9.64 2.56 2.2 0.090 0.67 -0.240

TechnologicalElectronic circuits

Undirected 24,097 53,248 4.34 11.05 3.0 0.010 0.030 -0.154

TechnologicalInternet

Undirected 10,697 31,992 5.98 3.31 2.5 0.035 0.39 -0.189

Technological Peer-to-peer network

Undirected 880 1,296 1.47 4.28 2.1 0.012 0.011 -0.366

n = number of nodesl = number of linksz = mean degreed = mean node-node distance

α = exponent of degree distribution if distribution follows a power-lawC = clustering coefficient r = degree correlation coefficient

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Software Applications

• Pajek• UCINET/NetDraw

– Analytic Technologies (Cambridge, MA)

• InFlow– Valdis Krebs, orgnet.com

• NetMiner• GUESS/Zoomgraph

– HP Labs

• NetLogo and RePast (ABM)• INSNA List

– http://www.insna.org/INSNA/soft_inf.html

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III. Examples and Applications

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Symantec Example• Computer Worm Simulator

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Terrorist Network Example

Courtesy Valid Krebs – orgnet.com

• Complex network analysis has been used to look at terrorist, criminal, and drug cartel networks

• News articles on the technique:– Clan, Family Ties Called

Key To Army's Capture of Hussein; 'Link Diagrams' Showed Everyone Related by Blood or Tribe (Washington Post, December 16, 2003)

– Six Degrees of Mohamed Atta, byThomas A. Stewart, (Business 2.0, December 01, 2001)

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Mark Lombardi Example

• Known for his “conspiracy art”

• Looked at the Iran-Contra Affair and links between global finance and international terrorism

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HP Email Example

Bernardo A. HubermanHP Senior Fellow and Director of the Information Dynamics Labhttp://www.hpl.hp.com/research/idl/

Week by week evolution of an email network

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Military Email Analysis Example

• Problem / Issue: Warfighters are faced with increasingly complex command and control (C2) networks

– Increasing number of IP networks, communication networks, and applications all creating a complex information environment

– Warfighter’s capability and effectiveness of new applications and networks are difficult to analyze

– Traditional C2 analyses limited to IT performance and human interface

• Possible Solution

– New complex network analysis techniques can now be applied to define the structure, dynamics and evolution of collaboration in command and control network

– Techniques enable the analysis of how warfighters actually use networks, as opposed to how engineers tell us how to build them

– Metrics can be used in defining and measuring new information architectures

©2005 Alidade Incorporated. All Rights Reserved

61

• Introduction of analysis method within CJTFEX 04-2 (a 12-day joint US/UK naval exercise)

• Analysis Focus - Email– The analysis is applicable to a wide range of

networks, email used as a stepping stone

– Email is the primary method of asynchronous electronic communication in the Information Age

– Indicates structures of collaboration and command and control

Military Email Analysis Example


62

Questions for Analysis

1. Does the email cross domain solution change previously established operating procedures?

2. Who are the key nodes for email traffic flow?

3. How robust is the email network in light of the removal of nodes and/or links?

4. How does the structure of the email network evolve over the course of the experiment?

5. What are the internal dynamics of select sub-networks and how to the sub-networks interact with each other?


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• We found: – CDS increased integration between US and UK

networks – Additional baseline information required to fully

define cross domain email need and use

• Method supports:– Defining role for individual liaison officers

Question #1Does the email cross domain solution (CDS) change previously

established operating procedures?


64

Aggregate Network of UK Interactions= UK= US

Question #1


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• Based on multiple metrics, we found:– J2 ACOS– Information Operations– Asst. JOC Watch

• Method supports:– Developing network defense for most important nodes– Providing input to plans for graceful degradation of

capability– Examining use of method to exploit adversary networks

and C2 structure

Question #2Who are the key nodes for email traffic flow?


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Collaboration Measures

1

10

100

1000

1 10 100 1000 10000

Out-Degree (kout)

In-D

egre

e (k

in)

Broadcasters

Receivers

Collaborators

Timeframe Receive Only

Xmit Only

Xmit & Receive

Day 6 1200-1800

684 (56%) 91 (7%) 441 (36%)

Day 8 1200-1800

894 (58%) 146 (10%) 504 (33%)

Question #2


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• We found:– Resilient to random node removal– Vulnerable to targeted node removal– Network structure makes rapid recovery possible

• Method supports: – Critical node placement in distribution of staff– Development of alternate C2 paths – Improving node counter-targeting

Question #3How robust is the email network in light of the removal of nodes

and/or links?


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Robustness MeasurementDetailed Timeframe – Day 8 1200-1800

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Number of Nodes Deleted

Siz

e o

f G

ian

t C

om

po

nen

t

Targeted Random

Degradation is not linear

Question #3


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Question #4How does the structure of the email network evolve over the course

of the experiment?

• We found:– Network structure follows staff daily battle rhythm,

significant events did not alter the network structure– Distance to get information from one person to

another remained roughly constant

• Method supports:– Re-engineering networks based on user behaviors to

assist in meeting warfighter requirements


70

Network Progression (Day 5)Question #4

= US & UK


71

• We found: – Structures of the sub-networks were very different from entire

CJTFEX email network, the CJTFEX was scale-free, the staff sub-networks were not

– Identifiable nucleus of communications in each staff– The two nuclei of Staff #1 and Staff #2 were well-connected– Using different link definitions (reciprocal, threshold) can provide

additional information about the network

• Method supports:– Development of techniques to split staffs between assets

Question #5What are the internal dynamics of select sub-networks and

how to the sub-networks interact with each other?


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Network DiagramStaff #2 Sub-Network Interactions – Entire Exp.

(Reciprocal Link Definition)

= nucleus node

Question #5


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Potential Futures Implications• William Gibson famously said that “the future is already here; it’s just

unevenly distributed”

• Futurists try to identify where critical distribution points in society are and monitor them for change – Futurists study emerging trends and new ideas in societies and how they

spread

– Futurists pride themselves on being able to identify early adopters at the beginning of the innovation “S-curve”

• Many tried and true techniques to perform these identifications – Environmental scanning, interviewing experts and trend-setters, etc.

• Techniques missing from the futurist toolbox are mathematical methods and models to determine how fast an idea, concept, or innovation will spread through a fixed network– Are there new rules, laws that we should know and codify?

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• In Duncan Watts’ book Six Degrees, he outlines a network theory-based explanation of how innovations are adopted by social networks

• Not only the predilection one has to change that determines success of an innovation, but also how many “neighbors” an individual has that have potential to exert influence

• Discovered that a determination of how likely innovations spread through a society can be made by examining a network for a large connected group of early adopters

• It is not the resilience of the individual, but network connectivity that is the primary obstacle to the diffusion of an innovation throughout society

• Success of innovations really has little to do with the actual innovation or innovator and more to do with the structure of the network that it is introduced in

Potential Futures Implications

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Potential Futures Implications

• Possible philosophical shift in futures thinking?

• A move away from discrete forecasting and scenario planning?

• “Instead of long-term planning, the aim should be to create the conditions most conducive to a process of continuous change.” – Chaos, Management And Economics: The Implications of Non-Linear

Thinking, David Parker and Ralph Stacey, 1994

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• Complex network principles are ones that all futurists should be familiar with

• Should we concentrate less on the “what” of the future and more on the “how” and “why”?

• Structure and process – Possibility Networks– Are we walking in the neighborhood of Hari Seldon?

• Discussion– What can we do with complex network theory?– Modifications of old tools, development of new tools– Role of APF in next steps

Potential Futures Applications

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IV. Demonstration

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Questions?

possibility networks

Technology