ETH D-GESS: 851-0585-37L, computer science (algorithms), sociology ... From “Information Theory of...

||Department of Humanities, Social and Political Sciences

Program in Computational Social Science

Social Modelling, Agent-Based

Simulation and Collective Intelligence(Week 7)

02.04.2016 1

ETH D-GESS: 851-0585-37L

Ovi Chris Rouly, PhD



ETH D-GESS: 851-0585-37L Week 7

02.04.2016Ovi Chris Rouly, PhD 2

Social Networks


Program in Computational Social Science02.04.2016Ovi Chris Rouly, PhD 3

This lesson considers social networks as abstract, mathematically

tractable, and computationally instantiable systems. We will look

at ways to model, instantiate, manipulate, and to analyze them.

Within the fields of computational social systems modeling, the

applied “deep-study” of Social Networks has become a discipline

unto itself. Moreover, its paradigms are based upon broadly

dissimilar scientific footings. To examine even a few of those

foundation stones we will have to consider mathematics (graph

theory), computer science (algorithms), sociology (population

group trends), psychology (individual and social behavior), and

complex networks.

Let’s get started!



Social Modelling, Agent-Based

Simulation and Collective Intelligence

Course Overview

Procedure (Parts I & II):

1. Examine a selection of published, formal models of social processes

2. Learn how to analyze and extend simple models and to develop your own social process models using existing computer-coded examples


Program in Computational Social Science02.04.2016Ovi Chris Rouly, PhD

Derived from “Introduction to Computational Social Science”, Cioffi-Revilla, 2014.

A Social Network as a Descriptor of Social Trends1. Nodes are elements within an abstract set

a. Individual object actors (animate, inanimate)

b. Ideas, symbols, groups-of-nodes, entire networks

2. Edges are possibly directed, always explicit, tangible/intangible relationships

a. Weighted bindingsb. Semantic bindings

c. Information-conduits

3. Aggregations are pregnant with implicit social meanings

a. Dyads

b. Triadsc. Cliques

4. Descriptive properties over a network include

a. Within and between element and network aggregations

b. Betweenness, centrality, and connectedness measures

c. Span, density, embeddedness, degreed. Simmelian ties, In-group/Out-group, and many others

d. “Clans”

e. Clusters

d. implicitly temporal



An abstract topology with implications for algorithm design and social modeling

A Network as an Abstract Topology and Social “Glue”

1. An agent can be associated with (mapped onto) a network node

(Here the agent moves only between nodes)a. An agent can move only if there is a connecting edge

b. An agent can move regardless of edge connections

2. A network node can be associated with (mapped onto) an agent

(Here the agent can move anywhere in raster, vector, or logical space)

a. An agent can move only if there is a connecting edge

b. An agent can move regardless of edge connections



From “Information Theory of Complex Networks”, Solé & Valverde, 2004, p. 4.

Regularity versus Complexity

ER = Erdos- Reyni

SF = Scale-Free



Networks: Abstract entities that are artifacts of social interaction

Relative Size versus Relative Complexity



“Error and attack tolerance of complex networks”, Albert, Jeong, Barabási, 2000.

Network Complexity versus Connectivity

(An Example: Exponential Network Compared to Scale-free Network)

Exponential(5 most connected nodes reach 27% of others)

Scale-free(5 most connected nodes reach > 60% of others)



Taken from “Towards Emergent Social Complexity”, Rouly, 2015, p. 124.

A Large, Regular, Artificial “Genealogical” Network

approx. 2,400 years



“How robust is the Internet?”, Tu, 2000.

A Large, Scale-Free, Human-made Network



G = { N, E, D }

where

• D is set of dimensions, {d1, d2, ... d|D|}

and each d is a triple over G

where

• dk ∈ D; 1 < k ≤ |D|

G = { N, E }

where

• G is a graph

• N is a set of nodes, {n1, n2, ... n|N|}

• E is a set of edges, {e1, e2, ... e|E|}

and an edge is a tuple over G

where ni, nj ∈ N; i ≠ j; i, 1 < j ≤ |N|

02.04.2016Ovi Chris Rouly, PhD

Quantitative operations over a network matrix can amplify social insight.

Social Networks as Multidimensional Graphs



Manipulation of the Information in a Social Network

Clearly, on a large network, the process of transcribing network

data from a “relationship graph” onto a matrix could be tedious.

But, once mapped onto a matrix, we can manipulate the network

algebraically and analyze the underlying system.

If we take this process one step further (automating the

transcription and putting everything in a “machine readable” form)

then, we can begin to do Social Network Analysis (SNA).

http://vlado.fmf.uni-lj.si/pub/networks/pajek/doc/pajekman.pdf



Measures exist to quantify properties of networks; some more useful than others.

Social Network Analysis – a self-describing process whose

intention is to identify meaningful features in a related set of artefacts

associated with social beings.

1. There exists no single “best measure” to describes a node (or an edge)

as most important in a network.

2. Measures exist to identify Bridging or Spanning nodes

3. Cliques and Clusters of nodes can be found and relative node Density

4. Measures of relative Connectedness and Centrality are numerous

For example:

a. Degree Centrality – how many edges attach to the node

b. Closeness Centrality – a node’s relative closeness to other

nodesc. Eigen (vector) Centrality – importance of a node influences the

importance of other nodes connected to it

d. Betweenness Centrality – situated placement in the network



That node whose central betweenness (CB) is greatest represents

among all possible paths between all other nodes, over all nodes in a

network, the most important. This is the “queen bee” of the network.

"... a point in a communication network is central to the extent that it falls on the shortest path between [all] pairs of other points" (Freeman, 1977).

Opinion:

While many network measures exist, central betweenness (CB) “may” be

the most important to us for understanding networks that seek to illustrate

the communication of ideas, substance, and information in general.

CB 𝑖 =

𝑗<𝑘

𝑔𝑗𝑘 (𝑖)

𝑔𝑗𝑘, 𝑖 ≠ 𝑗 ≠ 𝑘

X



Small World Networks are defined as those networks where the

distribution of the lengths (L) of all possible paths between all possible

nodes (N) in the network can be approximated by a log relation over the

number of nodes in the network. In particular, a Small-World Network will

have a relatively high coefficient of clustering (Ci) and a set of relatively low overall path lengths (e) over all nodes (i).

Opinion:

Among the naturally occurring network configurations, the Small-World

Network may be among the most important. It is a network type whose

interconnection configuration often emerges as an artifact associable with living systems. Watts & Strogatz (1998) pointed out they could be found in

structures as diverse as the, “neural network of the worm Caenorhabditis

elegans, the power grid of the western United States, and the collaboration

graph of film actors [movie stars] ...”.

L α log N



Clockwise from upper left:

LinkedIn network of DJ Patil (former chief scientist at LinkedIn)

A sexual network associated with an STD outbreak. Sexually Transmitted Infections,

Potterat et al. doi:10.1136/sti.78.suppl_1.i152

A social network in which clustering of body weight is visible; node size corresponds to

body weight, yellow nodes depict a BMI ≥30 (obese). The New England

Journal of Medicine, Christakis & Fowler doi:10.1056/NEJMsa066082

Taken from https://blogs.unimelb.edu.au/sciencecommunication/2012/09/25/its-a-small-world-after-all/

http://sti.bmj.com/content/78/suppl_1/i152.full.pdf+html



a spatial agent-based

model. And, we will talk

about how we could

integrate an agent-

based simulation (like

Schelling’s) together

with an abstract social

network.

Of course, we will also

propose a reading

assignment and discuss

the class deliverables.

After a break we will look at few example networks. We will also

discover that we now have many of the basic tools needed to build an

spatial agent-based model that incorporates a network-topology onto



5-6 minutes


break



Albert Einstein


"Things should be made as simple as possible - but no simpler."



Brief Primer: Social Psychology and Social Network Analysis

• Nodes – are the primary elements in a network. Their function in the network

is variously either “self” (ego) or “other” (alter). If “self” then, their purpose is

“self-motivated” action relative to their role and their subjective network

knowledge. If “others” their function is that of an arbiter or reactive agent.

• Edges – represent social connectivity in a network. They represent evidence of physical, informational, and or some other material or nonmaterial transfer

or contact between nodes. Typically edges suggest some social binding

between individuals and or groups of nodes. Finally, an edge often connotes

implicit temporal properties.

• Dyads – this is a two node network construct. Graphed together with an edgethey can show flow direction or not. Examples include:

• Triads – these closed network constructs have three nodes.

• Simmelian ties – (named for Georg Simmel) and extended by Krackhardt

(1999), are strong, bidirectional social bindings. Simmel thought that within a

triad having symmetrical Simmelian ties, the “self” would not be lost (Simmel & Wolff, 1950).

• Clique – a sub-network of three or more nodes having similar social purpose.



Network analysis tools reveal features often obscure but sometimes useful


Concepts:

Modeling paradigm – social networks

Analytic Tool – Pajek (others are available UCINet, RedSqirl, Gelphi, Cytoscape ...)

Process hypothesis – simple SNA can reveal hidden data insights

Networks: { Employees of: “IBM” &

“Google,” Customers of “Credit Suisse” &

“UBS,” and an amateur bicycle team }

Results*:

Centrality = 0.16363636

Degree = 5 (max)

Betweenness = 0.12644628

Most Connected = Harry & Credit SuisseMost Between = Credit Suisse* over all nodes

Analysis of our simple pedagogical social network



Concepts:

Modeling paradigm – multi-dimensional social network analysis

Analytic Tool – VOSViewer (others are available CitNetExplorer, CiteSpace, Histite ...)

Mechanism hypothesis – multi-dimensional SNA can reveal yet more data insights

Published in the Journal of the American

Society for Information Science and Technology

“... In our experimental analysis, we compare

three approaches for constructing bibliometric

maps... (Van Eck et al, 2010, p. 2).

In this example an analysis of the social

network data describes relationships between

authors, journals and keywords.

A comparison of two techniques for bibliometric mapping:

Multidimensional scaling and VOS (Van Eck, N., Waltman, L., Dekker, R.

& Van den Berg, J., 2010)



Authors

Journals

Keywords

“... In our experimental analysis, we compare three

approaches for constructing bibliometric maps...

(Van Eck et al, 2010, p. 2).

In this example an analysis of the social network

data describes relationships between authors,

journals and keywords.http://www.vosviewer.com/download



Concepts:

Modeling paradigm – complex networks

Process hypothesis – implicit system data exists in human social activity

Published in PLoS One

“A plausible approach to assess the

impact of a natural, large-scale disruption

is to measure systematic changes in the

distributional form of these standard

centrality measures. However, we find

that the functional form of degree, flux,

and betweenness distributions is

surprisingly robust to these disruptions as

illustrated in Fig. 2.” (Woolley-Meza et al,

2013, p. 3).

Eyjafjallajokull and 9/11: The Impact of Large-Scale Disasters on

Worldwide Mobility (Woolley-Meza, O. Grady D., Thiemann C., Bagrow, J. &

Brockmann, D., 2013)

“Figure 2. Network properties before and after

a natural disruption” (p.3). [P(b) is a measure of betweenness probability before disruption.]



Week 7 deliverable: Read then write to persuade or dissuade for SNA.


Reading assignments:

A chapter, if you want a know a little:

Scott, J. (1988). Social network analysis. Sociology, 22(1), pp. 109-127.

A book, if you want to know a lot more:

Scott, J. (2012). Social network analysis. Sage.

Writing assignment:

Write a 1-2 page White Paper arguing for (or against) the face validity of

using Social Network Analysis to describe the socio-political operations of

one of the individual country governments within the European Union. You will need at least two SNA citation/references to support your argument.

Nota bene: Any explicit reference to people or organizations *MUST* be

cited to, referenced by, no less than 2 other sources. Failure to adhere to

this requirement will result in a reduction of grade.

Deliverable in two weeks



• Albert, R., Jeong, H., & Barabási, A. L. (2000). Error and attack tolerance of complex networks.

Nature, 406(6794), pp. 378-382.

• Cioffi-Revilla, C. (2014). Introduction to computational social science: principles and applications.

Springer Science & Business Media. Chapter 4.

• Freeman, L. C. (1977). A set of measures of centrality based on betweenness. Sociometry, 35-41.

• http://faculty.ucr.edu/~hanneman/nettext/

• http://mrvar.fdv.uni-lj.si/pajek/

• http://vlado.fmf.uni-lj.si/pub/networks/pajek/doc/pajekman.pdf

• Krackhardt, D. (1999). The ties that torture: Simmelian tie analysis in organizations. Research in the

Sociology of Organizations, 16(1), pp.183-210.

• Batagelj, V., & Mrvar, A. Pajek–Program for Large Network Analysis. Home page: http://mrvar.fdv.uni-

lj.si/pajek/. (accessed on 11 March, 2016)

• Solé, R. & Valverde, S. (2004). Information theory of complex networks: on evolution and

architectural constraints. In Complex networks. Springer Berlin Heidelberg. pp. 189-207.

• Simmel, G. & Wolff, K. (1950). The sociology of Georg Simmel (Vol. 92892). Simon and Schuster.

• Tu, Y. (2000). How robust is the Internet?. Nature, 406(6794), pp. 353-354.

• Van Eck, N., Waltman, L., Dekker, R. & Van den Berg, J. (2010). A comparison of two techniques for

bibliometric mapping: Multidimensional scaling and VOS. Journal of the American Society for

Information Science and Technology, 61(12), 2. pp. 405-2416.

• van Eck, N. J., & Waltman, L. (2014). Visualizing bibliometric networks. (Chapter 13). In Measuring

scholarly impact. Springer International Publishing. pp. 285-320.

REFERENCES



• Watts, D. J. & Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature 393

(6684). pp. 440–442.

• Woolley-Meza, O., Grady, D., Thiemann, C., Bagrow, J. P., & Brockmann, D. (2013). Eyjafjallajökull

and 9/11: the impact of large-scale disasters on worldwide mobility. PLoS one, 8(8), e69829.

REFERENCES



consider theories about how opinions are formed and propagate

crowd disasters and ways to mitigate them

pedestrian traffic as emergent social phenomena

and, discuss Collective Intelligence and can it be instantiated

In the weeks that follow we will:



ETH Zurich

D-GESS Computational Social Science

Clausiusstrasse 50

8006 Zürich, Switzerland

http://www.coss.ethz.ch/

Ovi Chris Rouly, PhD.

Email: [email protected]

Telephone: (41) 044-633-8380

© ETH Zurich, 2 April 2016


Contact information

http://www.coss.ethz.ch/

mailto:[email protected]

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