Daniel Martin Katz (Illinois Tech - Chicago Kent) & Michael Bommarito (Computational Legal Studies.com) Present Network Analysis and Law: Introductory Tutorial @ Jurix 2011 (Vienna)
Daniel Martin Katz (Illinois Tech - Chicago Kent) & Michael Bommarito (Computational Legal Studies.com) Present Network Analysis and Law: Introductory Tutorial @ Jurix 2011 (Vienna)
How to conduct a social network analysis: A tool for empowering teams and wor...Jeromy Anglim
Slides and details available at: http://jeromyanglim.blogspot.com/2009/10/how-to-conduct-social-network-analysis.html
A talk on using social network analysis as a team development tool.
An introduction in the world of Social Network Analysis and a view on how this may help learning networks. History, data collection and several analysis techniques are shown.
Social Network Analysis: What It Is, Why We Should Care, and What We Can Lear...Xiaohan Zeng
The advent of the social networks has completely changed our daily life. The deluge of data collected on Social Network Services (SNS) and recent developments in complex network theory have enabled many marvelous predictive analysis, which tells us many amazing stories.
Why do we often feel that "the world is so small?" Is the six-degree separation purely imagination or based on mathematical insights? Why are there just a few rockstars who enjoy extreme popularity while most of us stay unknown to the world? When science meets coffee shop knowledge, things are bound to be intriguing.
I will first briefly describe what social networks are, in the mathematical sense. Then I will introduce some ways to extract characteristics of networks, and how these analyses can explain many anecdotes in our life. Finally, I'll show an example of what we can learn from social network analysis, based on data from Groupon.
Social Network Analysis Introduction including Data Structure Graph overview. Doug Needham
Social Network Analysis Introduction including Data Structure Graph overview. Given in Cincinnati August 18th 2015 as part of the DataSeed Meetup group.
How to conduct a social network analysis: A tool for empowering teams and wor...Jeromy Anglim
Slides and details available at: http://jeromyanglim.blogspot.com/2009/10/how-to-conduct-social-network-analysis.html
A talk on using social network analysis as a team development tool.
An introduction in the world of Social Network Analysis and a view on how this may help learning networks. History, data collection and several analysis techniques are shown.
Social Network Analysis: What It Is, Why We Should Care, and What We Can Lear...Xiaohan Zeng
The advent of the social networks has completely changed our daily life. The deluge of data collected on Social Network Services (SNS) and recent developments in complex network theory have enabled many marvelous predictive analysis, which tells us many amazing stories.
Why do we often feel that "the world is so small?" Is the six-degree separation purely imagination or based on mathematical insights? Why are there just a few rockstars who enjoy extreme popularity while most of us stay unknown to the world? When science meets coffee shop knowledge, things are bound to be intriguing.
I will first briefly describe what social networks are, in the mathematical sense. Then I will introduce some ways to extract characteristics of networks, and how these analyses can explain many anecdotes in our life. Finally, I'll show an example of what we can learn from social network analysis, based on data from Groupon.
Social Network Analysis Introduction including Data Structure Graph overview. Doug Needham
Social Network Analysis Introduction including Data Structure Graph overview. Given in Cincinnati August 18th 2015 as part of the DataSeed Meetup group.
Encuenta de Conocimiento de Computacion e Informatica, para hacer un calculo estadistico, u obtener personas de muestreo antes de llevar a cabo un Proyecto.
Distribution of maximal clique size of theIJCNCJournal
Our primary objective in this paper is to study the distribution of the maximal clique size of the vertices in complex networks. We define the maximal clique size for a vertex as the maximum size of the clique that the vertex is part of and such a clique need not be the maximum size clique for the entire network. We determine the maximal clique size of the vertices using a modified version of a branch-and-bound based exact algorithm that has been originally proposed to determine the maximum size clique for an entire network graph. We then run this algorithm on two categories of complex networks: One category of networks capture the evolution of small-world networks from regular network (according to the well-known Watts-Strogatz model) and their subsequent evolution to random networks; we show that the distribution of
the maximal clique size of the vertices follows a Poisson-style distribution at different stages of the evolution of the small-world network to a random network; on the other hand, the maximal clique size of the vertices is observed to be in-variant and to be very close to that of the maximum clique size for the entire network graph as the regular network is transformed to a small-world network. The second category
of complex networks studied are real-world networks (ranging from random networks to scale-free networks) and we observe the maximal clique size of the vertices in five of the six real-world networks to follow a Poisson-style distribution. In addition to the above case studies, we also analyze the correlation between the maximal clique size and clustering coefficient as well as analyze the assortativity index of the
vertices with respect to maximal clique size and node degree.
MODELING SOCIAL GAUSS-MARKOV MOBILITY FOR OPPORTUNISTIC NETWORK csandit
Mobility is attracting more and more interests due to its importance for data forwarding
mechanisms in many networks such as mobile opportunistic network. In everyday life mobile
nodes are often carried by human. Thus, mobile nodes’ mobility pattern is inevitable affected by
human social character. This paper presents a novel mobility model (HNGM) which combines
social character and Gauss-Markov process together. The performance analysis on this
mobility model is given and one famous and widely used mobility model (RWP) is chosen to
make comparison..
Using spectral radius ratio for node degreeIJCNCJournal
In this paper, we show that the spectral radius ratio for node degree could be used to analyze the variation of node degree during the evolution of complex networks. We focus on three commonly studied models of complex networks: random networks, scale-free networks and small-world networks. The spectral radius ratio for node degree is defined as the ratio of the principal (largest) eigenvalue of the adjacency matrix of a network graph to that of the average node degree. During the evolution of each of the above three categories of networks (using the appropriate evolution model for each category), we observe the spectral radius ratio for node degree to exhibit high-very high positive correlation (0.75 or above) to that of the
coefficient of variation of node degree (ratio of the standard deviation of node degree and average node degree). We show that the spectral radius ratio for node degree could be used as the basis to tune the operating parameters of the evolution models for each of the three categories of complex networks as well as analyze the impact of specific operating parameters for each model.
To have the ability to “think outside the box” is generally regarded as something positive. At a moment in time when resources are scarce, and the problems facing us are many, innovation and professional excellence becomes a requirement, rather than a matter of choice. At the core of our attempts to come up with new, and better solutions are the digital technologies. Within the structural engineering context, the different types of off-the-shelf packages for finite element analysis play a central role. These “black-box” types of software packages exemplify how user-friendliness may have harmful consequences within a field where knowledge and the successful mastery of relevant skills is key, and consequently- ignorance may lead to fatal results. These tools make any effort “venturing outside” difficult to achieve. A technical paradigm shift is called for- that places learning and creative, informed exploration at the heart of the user experience. Presented during the Knowledge Based Engineering session of the 19th IABSE congress entitled "Challenges in Design and Construction of an Innovative and Sustainable Built Environment" held in Stockholm, September 21-23, 2016.
To have the ability to “think outside the box” is generally regarded as something positive. At a moment in time when resources are scarce, and the problems facing us are many, innovation and professional excellence becomes a requirement, rather than a matter of choice. At the core of our attempts to come up with new, and better solutions are the digital technologies. Within the structural engineering context, the different types of off-the-shelf packages for finite element analysis play a central role. These “black-box” types of software packages exemplify how user-friendliness may have harmful consequences within a field where knowledge and the successful mastery of relevant skills is key, and consequently- ignorance may lead to fatal results. These tools make any effort “venturing outside” difficult to achieve. A technical paradigm shift is called for- that places learning and creative, informed exploration at the heart of the user experience. Presented during the Knowledge Based Engineering session of the 19th IABSE congress held in Stockholm, September 21-23, 2016.
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ICPSR - Complex Systems Models in the Social Sciences - Lecture 3 - Professor Daniel Martin Katz
1. Complex Systems Models
in the Social Sciences
(Lecture 3)
daniel martin katz
illinois institute of technology
chicago kent college of law
@computationaldanielmartinkatz.com computationallegalstudies.com
3. Stanley Milgram’s
Other Experiment
Milgram was interested in the
structure of society
Including the social distance
between individuals
While the term “six degrees” is often
attributed to milgram it can be traced to ideas
from hungarian author Frigyes Karinthy
What is the average distance
between two individuals in
society?
5. Six Degrees of Separation?
NE
MA
Target person worked in Boston as a stockbroker
296 senders from Boston and Omaha.
20% of senders reached target.
Average chain length = 6.5.
And So the term ...
“Six degrees of Separation”
6. Six Degrees
Six Degrees is a claim that “average path
length” between two individuals in society
is ~ 6
The idea of ‘Six Degrees’ Popularized
through plays/movies and the kevin bacon
game
http://oracleofbacon.org/
9. But What is Wrong
with Milgram’s Logic?
150(150) = 22,500
150 3 = 3,375,000
150 4 = 506,250,000
150 5= 75,937,500,000
10. The Strength of ‘Weak’ Ties
Does Milgram get
it right? (Mark Granovetter)
Visualization Source: Early Friendster – MIT Network
www.visualcomplexity.com
Strong and Weak Ties
(Clustered
v.
Spanning)
Clustering ----
My Friends’ Friends
are also likely to
be friends
11. So Was Milgram Correct?
Small Worlds (i.e. Six Degrees) was a theoretical
and an empirical Claim
The Theoretical Account Was Incorrect
The Empirical Claim was still intact
Query as to how could real social networks
display both small worlds and clustering?
At the Same time, the Strength of Weak Ties was
also an Theoretical and Empirical proposition
12. Watts and Strogatz (1998)
A few random links in an otherwise clustered
graph yields the types of small world
properties found by Milgram
“Randomness” is key bridge between the small
world result and the clustering that is
commonly observed in real social networks
13. Watts and Strogatz (1998)
A Small Amount of Random Rewiring or
Something akin to Weak Ties—Allows for
Clustering and Small Worlds
Random Graphlocally Clustered
16. 1 mode
Actor to Actor
Could be Binary
(0,1)
Did they
Co-Appear?
Different Forms of
Network Representation
17. Different Forms of
Network Representation
1 mode
Actor to Actor
Could also be
Weighted
(I.E. Edge Weights by
Number of
Co-Appearences)
18. Features of Networks
Mesoscopic Community Structures
We will discuss these next week
Macroscopic Graph Level Properties
We will discuss these today
Microscopic Node Level Properties
We will discuss these Next week
20. Shortest Paths
Shortest Paths
The shortest set of links
connecting two nodes
Also, known as the geodesic path
In many graphs, there are multiple
shortest paths
21. Shortest Paths
Shortest Paths
A and C are connected by
2 shortest paths
A – E – B - C
A – E – D - C
Diameter: the largest geodesic distance
in the graph
The distance between A and C is
the maximum for the graph: 4
22. Shortest Paths
I n t h e W a t t s - S t r o g a t z M o d e l
Shortest Paths are reduced by
increasing levels of random rewiring
24. Density
Density = Of the connections
that could exist between n nodes
directed graph: emax = n*(n-1)
(each of the n nodes can connect to (n-1) other nodes)
undirected graph emax = n*(n-1)/2
(since edges are undirected, count each one only once)
What Fraction are Present?
25. Density
What fraction are present?
density = e / emax
For example, out of 12
possible connections..
this graph
this graph has 7,
giving it a density of
7/12 = 0.58
A “fully connected graph has a density =1
26. Connected Components
We are often interested in whether
the graph has a single or multiple
connected components
Strong Components
Giant Component
Weak Components
27. “Largest Weakly Connected Component” in the
SCOTUS Citation Network
There exist cases that are not in this visual as
they are disconnected as of the year 1830
However, by 2009, 99% of SCOTUS Decisions are
in the Largest Weakly Connected Component
32. Degree Distributions
outdegree
how many directed edges (arcs)
originate at a node
indegree
how many directed edges (arcs) are
incident on a node
degree (in or out)
number of edges incident on a node
Indegree=3
Outdegree=2
Degree=5
33. Node Degree
from
Matrix Values
Outdegree:
outdegree for node 3 = 2,
which we obtain by summing
the number of non-zero
entries in the 3rd row
Indegree:
indegree for node 3 = 1,
which we obtain by summing
the number of non-zero
entries in the 3rd column
34. Degree Distributions
These are Degree Count for particular nodes
but we are also interested in the distribution
of arcs (or edges) across all nodes
These Distributions are called “degree
distributions”
Degree distribution: A frequency count of
the occurrence of each degree
36. Degree Distributions
Imagine we have this 8 node network:
In-degree distribution:
[(2,3) (1,4) (0,1)]
Out-degree distribution:
[(2,4) (1,3) (0,1)]
(undirected) distribution:
[(3,3) (2,2) (1,3)]
37. Why are Degree
Distributions Useful?
They are the signature of a dynamic process
We will discuss in greater detail tomorrow
Consider several canonical network models
47. Readings on Power law /
Scale free Networks
Check out Lada Adamic’s Power Law Tutorial
Describes distinctions between the Zipf,
Power-law and Pareto distribution
http://www.hpl.hp.com/research/idl/papers/ranking/ranking.html
This is the original paper that gave rise to
all of the other power law networks papers:
A.-L. Barabási & R. Albert, Emergence of scaling in random
networks, Science 286, 509–512 (1999)
50. How Do I Know Something
is Actually a Power Law?
51. Clauset, Shalizi & Newman
http://arxiv.org/abs/0706.1062
argues for the use of MLE
instead of linear regression
Demonstrates that a number
of prior papers mistakenly
called their distribution a
power law
Here is why you should use
Maximum Likelihood Estimation
(MLE) instead of linear
regression
You recover the power law
when its present
Notice spread between the
Yellow and red lines
52. Back to the Random Graph
Models for a Moment
Poisson distribution
Erdos-Renyi is the default random
graph model:
randomly draw E edges
between N nodes
There are no hubs in the network
Rather, there exists a narrow
distribution of connectivities
53. Back to the Random Graph
Models for a Moment
let there be n people
p is the probability that any two of them are ‘friends’
Binomial Poisson Normal
limit p small Limit large n
55. Generating Power Law
Distributed Networks
Pseudocode for the growing power law networks:
Start with small number of nodes
add new vertices one by one
each new edge connects to an existing vertex in
proportion to the number of edges that vertex
already displays (i.e. preferentially attach)
56. Growing Power Law
Distributed Networks
The previous pseudocode is not a unique solution
A variety of other growth dynamics are possible
In the simple case this is a system that extremely
“sensitive to initial conditions”
upstarts who garner early advantage are able to
extend their relative advantage in later periods
for example, imagine you receive a higher interest
rate the more money you have “rich get richer”