dynamic network analysis: some recent developments
•
•
Iscom 2004-2005 (April 4) drw
Overview: Networks, Scaling and a Complexity approach to Social Change.
Reconstructing Scientific Dialogue
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•
Models: Baseline, Applied Simulation, Longitudinal Data and Dynamical Models
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•
AJS
CMOT
Management Science
Ring Cohesion : Kinship ,e.g, Greek Gods
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•
Dynamics, e.g. Climate change as semiinteractive / semiexogenous
Industries and Lattices
GIS overlay
Network overlays (e.g., Royals and alliance dynamics)
Biotech
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–
–
•
General Theory
Network scaling - q-Exponentials
Feedback and Feedforward
Simulating trade
Simulating kinship
Simulating intercorporate networks
Strong Tie Small Worlds
Medieval to Modern (European Early Renaissance intercity network, 1175-1500)
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–
–
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•
Example:Agent Behavior; Applied Ramifications
A Baseline Model for Agent-Based Network Evolution: Ring Cohesion
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•
Example: Multiple Approaches to Temporal Scaling (Population, Economic Capital)
MSH [1]
MSH [2]
Generalized Computational machinery, Pajek
Not discussed: Nord-Pas-de-Calais industrial elite networks through time
–
Fractal network geography of social networks
focus on network dynamics in empirical and
simulated data
differentiate network models of temporal processes according to several distinctions
• 1. Baseline models, applied simulation models and empirical models.
•
2. Long-term data is not a longitudinal dataset and a longitudinal dataset does
not constitute a dynamic, or a dynamical view of a process. Longitudinal implies
that long-term data are cast into a framework for valid and linked comparison (e.g.,
tracking the same elements through time) and measuring change as well as static
variables. Dynamical implies a model of the process generating change, or, for that
matter, statis (e.g., self-canceling changes for a process at equilibrium).
•
3. Nondegenerate and degenerate network dynamics. The difference can be
illustrated by the relation of two variables in the phase space of the phenomena,
whether simulated or observed. In the degenerate case the two variables e, z are
related in a way that does not predict a change variable ż from the state variables
by some function ż = f(e,z). In a fully nondegenerate case such predictions can be
made for both change variables. Similarly for larger sets of variables. In a simple
Lotka-Voltera model for e chasing z and z chasing e, in a predator/prey model, for
example, ż = f(e,z) and ė = f(e,z).
Models
•
Baseline, Applied Simulation (trade; biotech; marriage; other networks),
Longitudinal Data and Dynamical Models
–
Baseline example:Agent behavior by node <s> in network N, modifying N
P(N´) = P(<s>|N, S, SP) x
(P(<s,t Є N>|s, N, S, SP) + P(<s,t ¢ N>)) i.e. P(t Є N) + (1-P(t ¢ N)
asynchronous update of N´ for selected <s>
selection of agent <s> proportional to degree kα of s.
selection of traversal of the agent’s token to <t> at an integer distance d from <s>
proportional to dβ, with d > 1. [agent tries to find a target via a token]
selection of each intermediate v from prior u in s-t path proportional to vγ.
Probability of network N´ within a class of networks formed from an existing N by
addition of a new edge from target node <t> to agent <s> either within N or
adding t to N, conditioned on structural properties of N in the set S, e.g.,
S={K,D,V}=degrees k of <i>, distances d of <s,t> and traversal properties of
s,…,u,v,…,t, adding exponential influence parameters on S in set SP ={kα,dβ,vγ},
Models, baseline
Example:Agent Behavior by node <s> within network N
In this example the interaction variables and their influence parameters
SP ={kα,dβ,vγ} correspond to activity of an agent ~ kα, the potency ~
dβ of the agent’s (token) communication and the strategy ~ vγ used
in token traversal, in which γ > 0 depends on the intelligence of
average nodes in the network as intermediaries in the transmission
of tokens in search of targets.
Interpretations: In general, an agent sustains itself by a search, first, for
a potential target t or partner with whom feedback is established
within an existing network, and, failing that, with a new partner t
Field properties: we look as distributions that asymptotically converge
as the asynchronous iterations  ∞. The convergent field processes
are brought back to make conceptual comparisons with processes
observed through time in smaller networks.
Models, baseline
Example:Agent Behavior by node <s> within network N
A selected agent s sustains itself by a search, first, for a potential target t or partner
with whom feedback is established within an existing network, and, failing that, by
recruiting and connecting to a new node t that serves as a resource
activity of an agent ~ kα,
potency ~ dβ of the agent’s (token) communication
strategy ~ vγ used in token traversal, in which > 0 depends on the average
intelligence of average nodes in the network as intermediaries in the transmission
of tokens in search of targets.
– Applied Ramifications: Interpretations in specific examples,
1 Interorganization ties in the biotech industry
2 Evolution of city networks in the Early European Renaissance
3 Emergence of coherent social units (class, ethnicity, industry cores and
scaffolds), including processes such as marriage
P(N´) = P(<s>|N, S, SP) x
(P(<s,t Є N>|s, N, S, SP) + P(<s,t ¢ N>))
consolidation
novelty
N=250
Edges
weighted by
traversals
forming
feedback
cycles
α=0
Left (γ=0), more novelty
γ=0
α=0
γ=1
Distance decay β =1.3
α=1
γ=0
α=1
γ=1
Lower (α=1), clustered
Right (γ=1), etched route
N=250
Nodes
weighted by
degree
Left (γ=0) ~ fewer cycles
α=0 γ=1
α=0 γ=0
Distance decay β =1.3
α=1
γ=0
α=1
γ=1
Lower (α=1) ~ airline hubs
Right (γ=1) ~ road circuits
networks and scaling
q-entropy (C. Tsallis) provides an accounting system for potential and kinetic
energies for both independent q=1 and nonindependent q≠1 interactions. Cycle
formation is produced by nonindependent probabilities: a final <v,u> link to
complete a cycle depends on a preexisting u-v path. For a baseline network
model of agency, with continuous probabilities, ought to have distributions that
are q-entropic and scale-free in q-entropic (log-q-log) measures.
Conjecture: Network dynamics will satisfy the laws of thermodynamics measured
by q-entropy, i.e., the study of the inter-relation between heat, work and internal
energy of a system, for independent and nonindependent interactions,
0
When two systems are in thermal equilibrium with a third body (like a thermometer),
they are also in thermal equilibrium (identical q-entropies) with each other
1
Energy can be changed from one form to another (heat, work and internal energy),
but it cannot be created or destroyed
2
In all energy exchanges, if no energy enters or leaves the system, the potential
energy of the state will always be less than that of the initial state (q-entropy nondecr)
3
The entropy of a perfect crystal at 0° K is zero
For many self-organizing systems, adaptive feedback (selection / intention) takes
place through cycle formation, while feed-forward occurs through storage
(etching) of traversal frequency as potential energy or information source for
future dynamics.
Theory of Ring Cohesion provides a structural accounting system for decomposing
feedback into agent-based behavioral generators
Simulations:
q=1.08
q=1.20
q=1.65
q=1.16
q=1.31
q=1.85
For α=1, β and γ
make little
difference, but
as α 0 the loglog scale-free
degree
distributions
almost always
shift to qexponential.
In a generalized
q-log-log scale
these are all
scale-free.
q=1.21
q=1.38
q=2.10
q=1.16
q=1.42
q=2.90
Simulations: All these distributions fit the q-exponential. For a given γ, α and β
make little difference to the q-exponential, but as γ  0, the distributions shift to a
decreasing concentration potential. γ  1 has greater concentration potential
from growth models to dynamics
a more general model incorporates decline along with
growth
S = (k, d, dist, Ai,j and Aj,i) has added structural measures
and the associated influence parameters expand to
SP = (α, β, γ, δ, ε) where α, β, γ are defined as before (for
k,d,v) and two new influence parameters govern the
probability bias on the deletion of a node or an edge:
selection of agent <s> for deletion proportional to degree kα of s, with δ
pos. or neg; alternatively, age specific mortality.
selection of edge <u,v> for deletion proportional to reciprocal edge
weight (Auv * Avu)ε, ε pos. or neg.
This model is capable of (mild) oscillatory dynamics that
can be amplified by cascade effects such as produced
by structural cohesion (meso-level network effects)
Feedback and feed forward
• Feedback is represented explicitely in the network agent
model: suggests that a replicator dynamic might weight the
replicative success of agents by the number of incoming
feedback cycles.
• The non-feedback edges, however, represent new
resources or sources of novelty.
• What is required for novelty to generate innovation,
however, is consolidation/reorganization. Replicator
dynamics (RD) might incorporate
– RD = f (feedback inputs, new ties, pairwise reciprocity resulting
from traversals, independent of agent objectives, nonindependent
cycles such as generalized reciprocity, and emergent higher order
organization). Ways in which directedness, e.g., may get washed
out.
Higher order interactions
• Why needed? The dynamic oscillations and
tipping points of observed network interactions
(trade, biotech, social networks) are more
exaggerated than the more continuous network
evolution models that add decay in small
perturbations. Are these random exogenous
shocks or endogenous network processes?
• Statistical analysis of new tie formation shows
that structurally cohesive aggregates have
effects independent of the micro attribute
predictions
dynamic role of structural cohesion
• A hierarchical embedded structuration with potentials for
intersections and organizations-in-fields crossovers.
• Biotech: structural cohesion provides the measure of level of
multiconnectivity in a cohesive core with a new tie and
novelty/consolidation dynamics.
• Marriage networks that define social class, ethnicity, wealth and
knowledge transition show similar patterns, as do trade networks.
• The consolidation processes of interaction in which significant
reorganization accomodates innovation are likely to occur within
structurally cohesive emergent units, e.g., David Lane’s recursive
“new attributions of functionality” and “forming new attributions.”
Bootstrapping proceses (Anderson 1972).
• As cohesive level goes up, by definition, size at that level goes down
in an intensifying shrinkage of reorganization. Cohesive
intensification in and of itself is thus also likely to be exclusionary
and potentially stultifying to further innovation.
Higher order interactions: how do
cohesive units emerge?
• Here is where feed-forward processes operate on
networks, because the etchings of traversal
frequencies create a mechanism for information
storage that influences future behavior through
agent perceptions (perceivable structures)
• Do these provide the endogenous network
processes needed to understand the dynamic
oscillations and tipping points of observed
network interactions (trade, biotech, social
networks) that are more exaggerated than the
more continuous network evolution models that
add decay in small perturbations.
Cohesive nodes (gold and red) in an expanded exchange network and further road
identification (red=3-cohesive) shows a second cohesive accumulation center further to
the east -- again, such cohesion supported the creation of wealth among merchants and
merchant cities, with states supported by indirect taxation and loans.
Red 3-components
Middle East and its
3-core not sampled
Now Northern Europe is represented (and the locations are geographic):
the main Hanseatic League port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice.
Betweenness Centralities in the banking network
(Net 6)
Betweenness centrality in
the trade network ought to
predict accumulation of
mercantile wealth. Genoa
has greatest wealth, as
predicted. On September 7th
1298 Genoa defeated the
Venetian fleet in battle.
Size of nodes adjusted
to indicate differences
in betweenness
centrality of trading
cities
(Net 7) Flow centrality (how much total network flow is reduced with removal of a node)
predicts something entirely different: the potential for profit-making on trade flows. It
necessarily reflects flow velocities central to the organizational transformations
undergone in different cities, as Spufford argues.
This type of
centrality is
conceptually very
difference and
distributes very
differently than
betweenness and
strategic centers
like Venice or
Genoa, which are
relatively low in
flow centrality.
(database now
expanded to
299 cities)
(Net3)
Productivities are
overlapping,
crosscutting and
interlaced in
complex ways
(Net3)
Productivities are
overlapping,
crosscutting and
interlaced in
complex ways
Note how an industrial "blue banana" construction is taking place with
communications in the left column, art works in the middle and linens on
the left, i.e., circulation among the NW-SE poles; while capitals show a
political vacuum of smaller polities in between, and trade fairs fill in this
vacuum by providing decentralized marketing institutions.
(Net3)
Productivities are
overlapping,
crosscutting and
interlaced in
complex ways
2005Iscom_Italy
D. R. White 2005
Engines of History
Innovation and Consolidation
PopPressure, Destruction, Cumulativity
… including power-law growth of world population.
3500
3000
Before
we go
there,and
it helps
In millions,
actual
trendto know that all
power-law growth entails strong predictions
from its singularity date (in this case 2030 ±
10) as the outer limit of sustained growth:
2500
2000
(1) It necessitates a transition before singularity
1500
(2) It predicts cycles of diminishing length as
singularity approaches
1000
500
0
-200
0
200
400
600
800 1000 1200 1400 1600 1800 2000
And if we take the departure from the trend to define
cycles of change we can begin to study other changes …
150
…we see cycles of population growth
100
Source:
White et al.
50
0
- 200 - 100
0
-50
100
200
300
400
500
600
700
800
900
1000 1100 1200 1300 1400 1500 1600 1700 1800
Detrended World Population to 1800, in millions
-100
0.15
-1500.1
0.05
-200
0
-200
-250
0
200
400
600
800
1000
1200
1400
1600
-0.05
-300
-0.1
Detrended as a percentage of prior population
-0.15
180
Reconstructing Scientific Dialogue: iscom-referential
eJournal communities, e.g., Structure & Dynamics, MBS
– Dialogic
– Review community
– Commentary, Reply, Replication
Example: Understanding Dynamics
–
–
–
–
Interaction models: classes of functions ż =f(a,b,c…)
Functions vs. exploring potential phase spaces
Measuremt. & experimental testing of unexplored spaces
Testing interactive dynamics vs. defects of curve fitting
Example: Multiple Approaches to Temporal Scaling
– Population
– Economic Capital
Example: Networks, Mesolevels, Scaffordings, etc.
– Iscom issues
Engine process: Territorial States
e.g., run by inputs of popPressure and
competition,
falling population
(innovations
outputs of
conserved)
Innovation T=
isolation
competition transport
(increase
Internal
with size) Conflict
(innovations)
Pop Density/Resources
P=Pop Pressure
This is Turchin's phase diagram for England, 1480-1800, for population size and sociopolitical
violence as a pair of variables that drive one another interactively. Temporal movement here
is clockwise (axes are reversed from the previous diagram). The dynamic is that the
population reaches carrying capacity setting sociopolitical violence into play, which only
recedes as population crisis leads to a collapse, leading into a new cycle.
‘Temperature’
‘Pressure’
Where you are on
this phase diagram
predicts where you
are going; this is
not true for
synchronously
correlated
variables
English sociopolitical violence cycles don’t directly correlate but lag population
cycles. Detrended English population cycles, 1100-1900, occur every 300-200 years.
Source:
Turchin
Chinese phase diagram
Turchin tests statistically the interactive prediction versus the inertial prediction for
England
Detrended Populations: World (logged)
(power law)
and England
0.15
Source:
White et al.
0.1
0.05
0
-200
0
200
400
600
800
1000
1200
1400
1600
1800
-0.05
-0.1
detrended
-0.15
4.0
3.0
Cycles grow shorter as predicted by
power-law growth.
England’s population cycles lag the World
cycles, which are heavily weighted by China
and India
2.0
1.0
0.0
-1.01000 1100 1200 1300 1400 1500 1600 1700 1800
-2.0
-3.0
-4.0
Correlates that
do not interact
dynamically
include:
Inflation cycles
(English: David
Hackett Fischer)
imitate
Renaissance
Equilibrium
(begins with
economic
depression)
Detrended
English
Population
cycles (Turchin)
1900
The population and sociopolitical crisis dynamic that drove Inflation also drove monetization
and trade in luxury goods in the 12th-15th centuries. Inflation of land value created migration
of impoverished peasants ejected from the land, demands of money rents for parts of rural
estates, and substitution of salaries for payments in land to retainers,
(Relative to Carrying Capacity)
Prices
Real wages
(low)
Inflation
In kind payment of serfs,
retainers salaried laborers
Demand for
prestige goods
Poverty forces more
meltdown of silver
Demand for
money rents
Peasants
to cities
Elites to cities
Conspicuous
consumption
Demand for
silver mining
Coinage
Monetization
(Velocity of Money in Exchange)
Effects of Inflation of Land
Thresholds
(Variables affecting transition)
on Monetization
Reorganization
(to handle higher velocities)
e.g., Division of labor, new techniques, road building, bridge building, new transport
Merchants/agents
Governments/agents
Churches/agents
Elites/agents
Engine processes
e.g., carnot cycles, run by inputs of fuel and
energy,
decompression
(momentum
outputs of
conserved)
momentum T
exhaust
firing
piston
and exhaust;
mechanically
(momentum)
linked
compression
P
Engine process: Biotech
e.g., run by inputs of cohesion and novelty,
outputs of
outside recruitment (novelty)
(innovation
innovation &
conserved)
distribution T=
internal
production couplings
Intra
distribution
Org.
(innovation)
Exchanges
cohesion
P= Cohesive Consolidation of Field
Cumulative ties, Biotech
Flip
these
back
and
forth
for
sense
of
dynam
ics
New ties, Biotech
0.8
New ties/Partner
0.7
New ties to partners ratio
0.6
versus
0.5
Core cohesion
Interactive dynamics between innovation
and consolidation (new ties  dense cores)
0.4
0.3
0.2
(Biotech)
time lags 1 & 2 yrsCohe
Percent organizations in top k-component (4, 5, 6)
0.1
0
1989
1991
1993
Cores get more
cohesive
( smaller) with time;
“high metabolism”
“more compact”
Geoff’s scaling laws
1995
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
1997
1999
Phase Diagram:
(New ties
for 1989)
Tree Ties
(1990)
Tree Ties
(1991)
Lots of
1992
Core
Tree Ties
Reinforce
ment
1992
Core
Reinforce
ment
Expanded
Core
Reinforce
ment
Expanded
Core
Reinforce
ment
Densified
Core and
Tree Ties
Densified
Core
Reinforce
ment
Densified
Core
Reinforce
ment
Tree Ties
Visually, we see in these last slides over 12 years a repetitive or cyclical dynamic
with 3-year cycleing:
new tie tree formation (reachout) for two years running,
but in the third year of each cycle –
new ties regroup to consolidate cohesion in the core.
Core reinforcement ratchets up to expanded core and then densified core.
These are the same patterns shown in the statistical analysis.
Field processes
• After a field influx of recruitment novelty
(absorbed into cohesive production) and
new recruitment falls to a minimum, it still
takes one year for the field to reorganize a
more cohesive core
• Takes two years for positive effects of a
more cohesive core to decay so as to
require influx of novelty through recruitment
nPart
newEntrants
e-new
year
e-new/nPart
new/100Entrants
Cohesion
%HiCohesive
672
29
362
1989
0.53869
0.12483
0.066
7.2
747
28
379
1990
0.507363
0.13536
0.063
7.2
792
18
379
1991
0.478535
0.21056
0.060
7.8
800
31
429
1992
0.53625
0.13839
0.025
2.9
873
35
520
1993
0.595647
0.14857
0.120
12.3
938
35
508
1994
0.541578
0.14514
0.130
13.7
985
24
543
1995
0.551269
0.22625
0.050
6.6
1058
34
737
1996
0.696597
0.21676
0.070
9.1
1172
14
696
1997
0.593857
0.49714
0.090
10.6
1313
13
957
1998
0.728865
0.73615
0.060
6.0
1332
12
1000
1999
0.750751
0.83333
0.055
5.5
estimated
estimated
0.9
0.8
0.7
0.6
e-new/nPart
e-new/100Entrants
Cohesion
0.5
Phase transition
to a condensed hi
metabolism core
0.4
0.3
0.2
0.1
0.0
1989
1991
1993
1995
1997
1999
From phase transitions to
Geoff’s scaling laws?
• The new animals (corporate cores 
emergent megacorporations)
• Encode elements of more dispersed lowerdensity systems (e.g., territorial)
• But now shrunk into a condensed and ‘high
metabolism’ form
• Higher ‘productivities’
• From bigger brutes to smaller powerhouses?
• One, but not the only way to evolve
Now look at R&D: Biotech
e.g., run by inputs of cohesion and novelty,
outputs of
outside recruitment (novelty)
(innovation
innovation &
conserved)
distribution T=
internal
production couplings
Intra
distribution
Org.
(innovation)
Exchanges
cohesion
P= Cohesive Consolidation of Field
0.8
0.7
New ties to partners ratio
0.6
0.5
Interactive dynamics between innovation
and consolidation (new ties  dense cores)
0.4
0.3
0.2
Percent organizations in top k-component (4, 5, 6)
0.1
0
1989
1991
1993
1995
1997
1999
R&D Should hit along with shifts of consolidation because
these are noticeable and create excitement, and diffusion out
of the core is maximum.
Now look at R&D (incomplete)
• Look at whether the fluctuations in R&D ties match the predictions
or fit in some other way into the dynamics (R&D/Finance data
below for 3 years prior to date shown. VC siphoned off to eComm
with internet bubble that started in 1995.
• Need the yearly data
0.800000
0.700000
0.600000
e-new/nPart
0.500000
Cohesion
0.400000
R&Dties
0.300000
FinancePartners
0.200000
0.100000
0.000000
1989
1991
1993
1995
1997
1999
structural cohesion in kinship
• Marriage networks that define social class,
ethnicity, wealth and knowledge transition
show similar patterns
Greek Gods: Census Graphs
Complex census graph for the selforganizing middle eastern network with
a maternal cluster (MBD) and a
paternal cluster (FBD)
Engine processes
e.g., carnot cycles, run by inputs of fuel and
energy,
decompression
outputs of
exhaust
T
exhaust
firing
compression
P
Specificity and stability in topology of protein networks
Sergei Maslov, Kim Sneppen
Science, 296, 910-913 (2002)
Specificity and stability in topology of protein networks
Sergei Maslov, Kim Sneppen
Science, 296, 910-913 (2002)