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Dynamic Network Analysis
Kathleen M. Cariey
Institute for Software Research International
Carnegie Mellon University
Abstract
Dynamic network analysis (DNA) varies from traditional social network analysis in that it can
handle large dynamic multi-mode, multi-link networks with varying levels of uncertainty. DNA,
like quantum mechanics, would be a theory in which relations are probabilistic, the measurement
of a node changes its properties, movement in one part of the system propagates through the
system, and so on. However, unlike quantum mechanics, the nodes in the DNA, the atoms, can
learn. An approach to DNA is described that builds DNA theory through the combined use of
multi-a=,ent modeling, machine learning, and meta-matnx approach to network representation. A
set of candidate metric for descnbing the DNA are defined. Then, a model built using this
approach is presented. Results concerning the evolution and destabilization of networks are
described.
Acknowledgement
The research reported herein was supported by the National Science Foundation NSF IRI9633
662, the Office of Naval Research (ONR) Grant No. N00014-97-~-0037 and Grant No.
9620. ~.l 140071, Additional support was provided by the NSF IGERT 9972762 for research and
training in CASOS and by the center for Computational Analysis of Social and Organizational
Systems at Carnegie Mellon University (http://www.casos.ece.cmu.edu ). The views and
conclusions contained in this document are those of the authors and should not be interpreted as
representing the official policies, either expressed or implied, of the Office of Naval Research,
the National Science Foundation or the U.S. government.
DYNAMIC SOCIAL NETWO~MODEL~G ED ^^YSIS
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Dynamic Network Analysis
Terrorist organizations have network structures that are distinct from those in typical
hierarchical organizations - they are cellular and distributed. While most commanders,
politicians and intelligence agents have at least an intuitive understanding of hierarchies and how
to affect their behavior, they have less of an understanding of how to even go about reasoning
about Dynamic networked organizations (Kontelt and Arquilla, 20011. It is even more difficult
for us to understand how such networks will evolve, change, adapt and how they can be
destabilized.
_ 1_ ~ 1 . ~
Clearly social network analysis can be applied to the study of covert networks (Sparrow,
19911. Many are stepping forward suggesting that to understand these networks we just need to
"connect the dots" and then isolate the "key actors who are often defined in terms of their
"centrality" in the network. To an extent, this is right. However, it belies the difficulty of
"connecting the dots" in terms of mining vast quantities of information, pattern matching on
agent characteristics for people who go under multiple aliases, and still ending up with
information the may be intentionally misleading, inaccurate, out-of-date, and incomplete.
Further, this belies the difficulty in "knowing" who is the most central when you have at best
only a sample of the network. Finally, and critically, this approach does not contend with the
most pressing problem - the underlying network is dynamic. Just because you isolate a key
actor today does not mean that the network will be destabilized and unable to respond. Rather, it
is possible, that isolating such an actor may have the same effect as cutting off the Hydra's head;
many new key actors may emerge (CarIey, Lee and Krackhardt, 2001~.
To understand He dynamics of terrorist, and indeed any, network we need to understand the
basic processes by which networks evolve. Moreover, we have to evaluate isolation strategies in
the face of an evolving network and in the face of missing, information. To ignore either the
dynamics or the lack of information is liable to lead to erroneous, and possibly devastatingly
wrong, policies. Taking in to account both the dynamics and the lack of information should
engender a more cautious approach in which we can ask, "if we do x what is likely to happen?"
L`i~tations to Traditional SNA
Traditionally, social network analysis (SNA) has focused on small, bounded networks, with
2-3 types of links (such as friendship and advice) among one type of node (such as people), at
one point in time, with close to perfect information. To be sure there are a few studies that have
considered extremely large networks, or two types of nodes (people and events), or unbounded
networks (such as inter-organizational response teams); however, these are the exception not the
norm. However, such studies are still the exception not the rule. Further, while it is understood,
at least in principle how to think about multi-modal, multi-plex, dynamic networks, the number
of tools, the interpretation of the measures, and the illustrative studies using such "higher order"
networks are still in their infancy relative to what is available for simpler networks. Finally,
many of the tools do not scale well wig the size of the network or degrade gracefully with errors
in the network; e.g., they may be too computationally expensive or too sensitive to both type ~
and 2 errors. What is needed is a dynamic network analysis theory and toolkit. We are working
134
DYNAMIC SOCKS N~TWO=MODEL~G ED ISIS
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to develop such a tool kit and the associated metrics and decision aids. In this paper. one such
tool, DyNet is described and used to examine various isolation strategies.
Dynamic Network Analysis
Recently there have been a number of advances that extend SNA to the realm of dynamic
analysis and multi-color networks. There are three key advances: I) the meta-matrix, 2) treating
ties as probabilistic, and 3) combining social networks with cognitive science and multi-agent
systems. These advances result in a dynamic network analysis.
Meta-Matnx: CarIey (2002) combined knowledge management, operations research and
social networks techniques together to create the notion of the meta-matnx - a multi-color,
multiplex representation of the entities and the connections among them. The Meta-matr~x is an
extension and generalization of the PCANS approach forwarded by Cariey and Krackhardt
( 1999) that focused on people, resources and tasks. For our purpose, the entities of interest are
people, knowledge/resources, events/tasks and organizations - see table I. This defines a set of
10 inter-linked networks such that changes in one network cascade into changes in the others;
relationships in one network imply relationships in another. For example, co-membership in an
organization or co-attendance at an event for two people suggests a tie in the social network
between these two people. A group, such as a terrorist network, can be represented in terms of
an overtime sequence of such networks. In fact, any organization or group can be represented in
this fashion and we have used this representation on numerous occasions to characterize actual
organizations and to predict their ability to adapt.
All graph theory and network measures can be defined in terms of whether they can or have
been applied to which cells. Further, on the basis of this meta-matr~x new metrics can be
developed that better capture the overall importance of an individual, task, or resource in the
group. An example of such a metric is cognitive load - the effort an individual has to employ to
hold his role in the terrorist group - and it takes in to account, who he interacts with, which
events he has been at, which organizations he is a member of, the coordination costs of working
with others in the same organization or at the same event or in reaming from an earlier event or
training for an upcoming event. A large number of such metrics have been developed and
analyzed in terTns of their ability to explain the evolution, performance, and adaptability of
dynamic networks.
A key difficulty from a growth of science perspective, is that as we move from SNA to DNA
the number, type, complexity, and value of measures changes. A core issue for DNA is what are
the appropriate metrics for describing and contrasting dynamic networks. Significant new
research is needed in this regard. To date, our work suggests that a great deal of leverage can be
gained in describing networks by focusing on measures that utilize more of the cells in the meta-
matnx. For example, cognitive load, which measures the cognitive effort and individual has to
do at one point in time has been shown to be a valuable predictor of emergent leadership (Cariey
and Ren, 20011. Cognitive load is a complex measure that talces into account the number of others,
resources, tasks the agent needs to manage and the communication needed to engage in such activity.
In addition, we find that for any of the cells in the meta-matrix, particularly for large scale networks.
many of the standard graph level measures have little inflation content as the network grows in
size (Anderson, Butts and CarIey, 1999) andfor are highly correlated with each other. A set of
measures that are generally not correlated, scale well, and are key in characterizing a network are the
DYNAMIC SOCIAL NETWOI?KAdODEL~G~D ISIS
135
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size of the network (number of nodes), density (either as number of ties or the typical social network
form number of ties/number of possible ties), homogeneity in the distribution of ties (e.g., the
number of clusters or subcomponents, the variance in centrality), rate of change in nodes, and rate of
change in ties. The point is not that these are the only measures needed to characterize dynamic
networks. The point Is that these are a candidate set that have value and that as a field we need to
develop a small set of metrics that can be applied to networks, regardless of size, to characten~:e the
dynamics.
Table I. Meta-Matnx
. . ..
People Knowledge/Res Events/Tasks
ources
. .
Social network Knowledge Attendance
network network
.
Information Needs network
network
Temporal
ordering
Organizations
People
Membership
network
Organizational
capability
Institutional
support or
attack
Knowledge/Res
ources
Events/Tasks
Organizations
Inter-
organizational
network
Probabilistic Ties: The ties in the meta-matnx are probabilistic. Vanous factors affect the
probability, including the observer's certainty in the tie and the likelihood that the tie is manifest
at that time. Bayesian updating techniques (Dombroski and CarIey, 2002), cognitive inferencing
techniques, and models of social and cognitive change processes (CarIey, 2002; CarIey, Lee and
Krackhardt, 2001) can be used to estimate the probability and how it changes over time. We are
in the process of exploring techniques for combining the cognitive inferencing with the cognitive
change process models.
Multi-Agent Network Models: A major problem with traditional SNA is that the people in
the networks are not treated as active adaptive agents capable of taking action, learning, en c!
altering their networks. There are several basic, well known, social and cognitive processes that
influence who is likely to interact with whom: relative similarity, relative expertise, and co-
worker. CarIey uses multi-agent technology in which the agents use these mechanisms, learn,
take part in events, do tasks to mode! organizational and social charge. The dynamic social
network emerges from these actions. The set of networks linking people, knowledge, tasks and
other groups or organizations co-evolve. CarIey, Lee and Krackhardt (2001) use simple learning
mechanisms to dynamically adjust networks as the agents in them attended events, learned new
information, or were removed from the network. In DyNet, described herein, additional
mechanisms center on agent isolation are also considered.
DNA has a wide ran3e of applications. For example, this approach is being used to examine
the likely impact of unanticipated events in the VISTA project (Died~ch et al, forthcoming), the
possible effects of biological attacks on cities in BioWar (Carley et al, 2002)? in evaluating CIO
response strategies to denial of service attacks (Chen, 2002), and evaluating information security
136
DYNAMIC SOCIAL NETWO~MODELING AND ANALYSIS
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within organizations - ThreatFinder Project (Cariey, 20011. See also www.casos.ece.cmu
current projects and working papers.
Dynamic Network Theory
To move beyond representation and method, we need to ask, "How do networks change?,'
What are the basic processes? From the meta-matrix perspective, the processes are easy - things
that lead to the adding and dropping of nodes author relations - see table 2. Again, no claim is
being made that the processes listed in table 2 cover the complete spectrum; rather, they illustrate
the types of node change processes that need to be postulated. A full theory of dynamic
networks needs to speak to such mechanisms.
People
Table 2. Basic Change Processes for Nodes in the Meta-Matrix
_
Knowledge/Resources Events/Tasks
Innovation Goal Change
Discovery Re-en~neering
Forgetting Development of new
Cons umption technology
Stop usage of
I technology
Birth
Death
Promotion
Mobility
Recruitment
Incarceration
Isolation
Organizations
Organizational birth
Organizational death
Mergers
Acquisitions
Legislation of new
entity
Similarly, there are a set of processes that lead to the addition and removal of relations.
Basic processes are cognitive, social and political in nature. Cognitive processes have to do with
learning and forgetting, the changes that occur in ties due to changes in what individuals know.
Social changes occur when one agent or organization dictates a change in ties, such as when a
manager re-assigns individuals to tasks. Finally, political changes are due to legislation that
effect organizations and the over-arching goals. To illustrate what is meant, a limited number of
such processes are described in Table 3. Fumier, and this should be obvious, processes that add
or eliminate nodes also affect relations to/from that node. For example, if all individuals in a
society forget a particular piece of information that knowledge node, no longer exists and all
connections frown people to it are now eliminated.
DYNAMIC SOCIAL NETWORK MODELING ED ANALYSIS
137
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Table 3. Chance Processes for Relations in the Meta-Matrix
People Knowledge/ Events/ Tasks
Resources
Motivation to Learning Re-assignment
Interact Acquisition
Change in
access
Discovery Innovation
Analogical
reasoning
~ . .
Organizations
People
Mobility
Recruitment
Knowledge/
Resources
Events/Tasks
Organizations
DyNet
IP development
Re-engineenng
Out-sourcing
Alliances
Coalitions
The purpose of the DyNet project is to develop the equivalent of a flight simulator for
reasoning about dynamic networked organizations. Through a unique blending of computer
science, social networks and organization theory we are creating a new class of tools for
managing organizational dynamics. The core tool is DyNet - a reasoning support too] for
reasoning under varying levels of uncertainty about dynamic networked and cellular
organizations, their vuInerabilities, and their ability to reconstitute themselves. Using DyNet the
analyst would be able to see how the networked organization was likely to evolve if left alone,
how its performance could be affected by venous information warfare and isolation strategies,
and how robust these strategies are in the face of varying levels of information assurance.
138
DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS
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Database of
Organ izational \ Network
Scenarlos \ Profile
\ Aback
Characteristics ~ Scenario
Of known or /
Hypothetical / Individuals =
Network or ~ Observe
Cellular Dynamics
Organization
I.
Critic al -
DYN ET
,
-
~ 00 ~
\ I~—._.,
l,(7
..
,—
Figure I. DYNET: A desktop too! for reasoning about dynamic networked and cellular
Organlzatlons.
DyNet is intended to be a desktop system that can be placed in the hands of intelligence
personnel, researchers, or military strategists. Through hands-on what if analysis the analysts
will be able to reason in a what -if fashion about how to build stable adaptive networks with high
performance and how to destabilize networks. There are many applications for such a too!
including: threat assessment, assessing information security risks in corporations; inter training;
simulation of the red team in a gaming situation, and estimation of efficacy of destabilization
policies. Currently an alpha version exists as a batch program (no visualization) and it has been
used to evaluate simple isolation strategies. The system can handle data on real networks.
The DyNet too} is a step toward understanding how networks will evolve, change, adapt and
how they can be destabilized. The goal will be to incorporate all of the evolutionary mechanisms
previously discussed. DyNet, which is a computer mode] of dynamic networks, can also be
thought of as the embodiment of a theory of dynamic networks. The focus of this theory is on
the cognitive, and to a lesser extent, social processes by which the networks in the meta-matnx
evolve. The basic cognitive forces for change in DyNet are learning, forgetting, goal-setting, and
motivation for interaction. The basic social forces for change are recruitment, isolation, and to a
limited extent the initiation of rumors and training.
The basic motivations for interaction are relative similarity, relative expertise or some
combination of the two. Relative similanty is based on the fundamental finding of homophilly,
the tendency of interacting partners to be similar. Arguments surrounding this fundamental
process include the need for communicative ease. comfort, access, and training. Relative
expertise is based on the fundamental finding that when in doubt people will turn they view as
experts for information. Arguments surround this fundamental processes include the need to
acquire, desire to minimize search, desire to optimize information, and so on. Other basic
motivations such as the need to exhibit competence and the need to coordinate have also been
identified and will be added to DyNet but are not in the current system.
Among the attrition strategies are removal of the most "central" individual, removal of the
individual with the highest cognitive load, and removal of individual's at random. User's can
control the frequency and severity of such attrition strategies. Previous studies using this system
have shown that a) it is difficult to completely destabilize a network, by that the best strategy
DYNAMIC SOCL4L NT:TWORK MODELING AND ANALYSIS
139
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depends on the structure of the network and c) attrition strategies vary in whether there
effectiveness is enhanced or diminished by removing multiple agents at once or sequentially
(CarIey, 20021.
Agents can be distinguished based on fixed characteristics such as race, family and gender,
and on knowledge (or training). Further, the agents can operate in a world without information
technology or augmented by access to email, web pages, or manuals. Access to others can be
restricted, as might be the case when operatives live in different countries. Performance metrics
include task completion, accuracy, energy for tasks, information diffusion, and group cohesion.
Finally, the basic networks can be extracted continually ire order to see the system evolve.
Among the networks that can be extracted are the knowledge network, the overall social
network, the emotive or "friendship" networks, and the acquisition or ~'advice" network. The
network evolutionary strategies include learning (during interaction), forgetting, personnel
attntion, misinformation, and changing task demands. DyNet offers the user the choice of
entering specific networks or entering network characteristics (such as size and density).
Results
Using, DyNet a series of virtual experiments were run. These experiments were designed to
examine the interaction between network structure, dynamics (particularly in response to
isolation), and the information that the observer has on which to base the isolation strategies. In
figure 2, a very high level conceptualization of these differences is shown. Three possible
isolation strategies: isolating individuals at random, isolating those who are the most central
(degree centrality), and isolating those with the highest cognitive toad are shown relative to a
specific organization and networks within it. Given that the networks are evolving at issue is
which of these strategies will be the most effective? Further, we might ask, if the social network
was different, e.g., less hierarchical, would that matter?
. —
·= : . ~ ~ ~ - ,
,~)Highest Centrality ~
'~"~
~ ~] Highest Co~,nit~e Mad
~~ .--'/
sit
Figure 2. Structure, Isolation and Dynamics
140
DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS
Random
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The Structure of the Network Matters
The first finding, and it is quite robust, is that the structure of the network matters. That is,
random networks in which the relations are distributed in an independent and identical fashion?
hierarchies, and cellular networks all evolve quite differently, require different strategies to
destabilize, have different abilities to diffuse information, and exhibit different performance for
the same task. In Figures 3 and 4. this difference is illustrated with respect to the networks
ability to recover from isolation strategies. In figure 3 we see the impact of the three isolation
strategies on a random lid network and in figure 4 the impact of the same strategies on a cellular
network. As an aside, the particular cellular network simulated here is one whose features map
onto available information about covert networks, such as the cells are completely connected
internally and cell size ranges from 3-10 members. In these figures not only do we see that the
isolation strategies vary in their effectiveness based on the structure of the network they are
attacking, but in addition, cellular networks are able to recover from the attacks.
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A second key findin, is that networks are generally able to heal themselves. That is isolation
of a node that links disparate groups together typically does not leave those groups disconnected.
Rather the basic social and cognitive processes outlined lead individuals to seek alternative
contact points to interact with. For example in Figure 5 we see on the left a network where the
person with the highest cognitive [load, the emergent leader was isolated. A consequence is that
multiple new leaders emerge, each of whom ends up being more directive than the original
leader. Healing is not guaranteed and in fact depends on the underlying structure, the cultural
basis for interaction? the degree of isolation, the frequency of isolation, and the strategy for
isolation. For example, as was seen in Figure 4, cellular networks he e] themselves regardless of
which isolation strategy is used against it. in this case, the cell structure of the network enables
DYNAMIC SOCKS NETWO=MODEL~G ED TRYSTS
141
OCR for page 142
the network as a to engage in what appears as "meta-learning," i.e., learning how to recover from
unanticipated attrition. Cellular networks, which are the structure most like those used by
terrorist organizations, are very difficult to destabilize. The reasons are complex, but a key
factor is that such network structures are able to heal relatively faster than other structure both in
teens of the re-emergence of leaders and in teens of performance recoveries after personnel have
been removed.
Full Information is Not Necessary
In the foregoing two examples, we saw the impact of destabilization strategies on network
without considering "how is it that we know what we know?" Or in other words, "if we are not
sure what the underlying network looks like, how confident can we be in our predictions about
how to destabilize it?" Notice, that in traditional SNA, typically we have close to full
information. For covert networks we do not. Information may be missing because we don't
know some of the nodes - the people involved, or because we don't know some of the relations.
C?
_~
.. . ... ... .. _
.. _ . ~ (5,_
/~
~ (c ~~ ~~3:-
o~
. . .-
-
-
~0 (5)
v
,. ~
Figure 5. The network before (left) and after (right) the isolation of the leader.
Figure 6. The impact of incomplete information about who is in the network.
In Figure 6
we see the
impact of not
knowing al the
nodes. Here
we see the
. ~
comparison ot
no attack,
versus the
average impact n o - is o la tic n
of isolating
personnel
31
30
2 9 '_ _
l
2 8
25
142
Ad:
it'
Pe rf 0 r m a n c e
perfect 90% people 75% people 50% people
know ledge
DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS
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(across the three isolation strategies under conditions of full information, knowing 90% of the
nodes, 75~o and only 50%. Clearly having close to perfect or perfect knowledge means that
more effective isolation strategies are found. Note, however, that any isolation is better than
none, assuming our goal is to degrade the performance and that we don't need perfect
information to be quite effective.
Now, consider the case where we don't have perfect information about the relations. One
way for this to occur is if we don't know all the knowledge or resources that are available to the
network. In figure 7 we see the impact of having imperfect knowled Be of the relations as a
function of how much do we know about the other entities, in this case what there is for the other
to know. Here we see that we actually do better knowing less. This is due to the interaction
between what we know and the isolation strategy. Essentially, when we don't really know the
underlying social and knowledge network we may overestimate the primacy of a person. who
although not the key in terms of degree centrality, is more central in terms of cognitive load.
Thus, in effect, less knowledge makes both the centrality and the cognitive load strategies more
similar resulting in on average lower performance due to the fact that cellular networks are more
devastated by the extraction of such emergent leaders, at least in the short run. Further, reduced
information about relations makes all isolation strategies more mixed thus inhibiting the ability
of the opponent to engage in meta-learning.
Figure 7. The impact of incomplete information about what people know.
30
29
27
26
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..._.. _.... __ ....... _._..._..... ...._.._ _ ......_ ._ _ __.._ .. _ _..._...._ _...___ ___ ... _......... ~......_... _....... ... ~ _.......... _... _........... _ ...
Perform ance
31 --
1~
2: ~~e~(-l~
Perform anon
no-isolation perfect knowledge 90% knowledge
Summary
75% knowledge
50% knowledge
, .
Thinking about networks from a dynamic perspective is absolutely essential to understanding
the modern world. An approach toward dynamic networks has been outlined. There are several
distinctive hallmarks to this approach. First, in contrast to other multi-agent work, the agents we
describe are in actual social networks. Here, the networks and the agents co-evolve. Secondly,
the web of affiliations connects not just agents. but agents and other entities such as knowledge,
tasks and organizations. The agents described here in are more cognitively realistic than the
typical a-life agents. They are also more socially realistic in teIms of interaction than the typical
e-commerce agents as the agents we use are boundedly rational rather than optimizers. Another
distinction compared to most systems is that DyNet can take real networks as input.
DYNAMIC SOCIAI~ N~TWORKMOD~L~G ED CYSTS
143
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In contrast to traditional SNA, DNA considers the role of the agent in terms of processes and
not just position. That is, the agents can do things - communicate, store information, learn.
Further, the networks are dynamic and changing even as the agents change. The links ar
probabilistic the networks multi-colored and multi-plex to the extent that the set of networks
combine in to one complex system where changes in one sub-network inform and constrain
charges in the others, often leading to error cascades. Finally, DNA explores the sensitivity of
the measures and the impacts to error.
The approach, theory, and results described here are illustrative. Clearly much work needs to
be done before we have a complete understanding of network dynamics. Are there likely to be
other change mechanisms than those currently in DyNet - to be sure. However, since all human
action is cognitively mediated - it is unlikely that such mechanisms will not be denvable, at a
basic level from what the physical and physiological constraints, what the agent knows, the basic
learning and information processing mechanisms, and the way in which groups. organizations
and institutions store such information. To create a truly dynamic network theory we need to
create the equivalent of a quantum dynamics for the socio-cognitive world, where the
fundamental entities, the people, unlike atoms, have the ability to learn.
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Representative terms from entire chapter:
isolation strategies
