Preso on social network analysis for rtp analytics unconference

Consolidated Behaviors and Attitudes1
Analyzing Networks
An Overview, and Discussion of Network
Analysis (NA) and Social Network Analysis (SNA)
Prepared for 2013 AnalyticsCamp:
An Annual Unconference , Held in the
Research Triangle Park, NC Area, on May 4, 2013
By Bruce Conner
Consolidated Behaviors and Attitudes

Full Disclosure
• I just finished the Social Networking course,
on Coursera, taught by Lada Adamic, Assoc.
Prof. of Information at the Univ. of Michigan
– All of the content of this deck is derived
from that course (not original)
– For purposes of this unconference, I will
not be further citing or footnoting this
content

My Interest in Social Networking Analysis (SNA)
• Interest in marketing analytics and quantitative market research
– Rise of social media and social marketing
– Big data and marketing analytics
– The strengths and weaknesses of behavioral data (Web, mobile, CRM,
transactional, scanner, telemetry, etc.) in marketing applications
• A long-term interest in clustering and segmentation as tools of
identifying and targeting of products, services, and messages: can
social relationships and social communities enhance this?
• Marketing issues such as:
– The role of opinion leaders in influencing brand preferences and purchases of
goods and services
– Diffusion of products, services, innovations, brands, preferences, etc.
– Formation of preferences for products/services/brands
– Targeted marketing to communities and individuals in those communities

Agenda
• Brief introduction to the applications and issues that
Social Networking Analysis (SNA) – and, more broadly
Network Analysis (NA) -- try to deal with
• Brief overview of some methods, approaches, and
statistics involved
• Possible Discussion Topics:
– Who is currently using SNA (or NA) -- and what are your
applications?
– How (else) might SNA (or NA) be used in your work?
– Specifically, how might SNA (or NA) be used in marketing,
product development, or other business applications (or
other applications
– Other topics/questions/thoughts?

Quick Overview of SNA Applications

Quick Overview of Applications of SNA:
Anti-Terrorism and National Security

A Quick Overview of
Applications of SNA (2)
• Anti-terrorism
• Criminal justice
– Conspiracy (e.g., Enron)
– Insider trading
– Fraud

A Quick Overview of
• Anti-terrorism
• Social media

A Quick Overview of
• Anti-terrorism
• Social media
• Gaming
–Game (Social) Experience
–Recruitment/virality/engagement/
retention/conversion

And Some More
• Organizational analysis/
communities of practice
• Marketing based on affiliation
with “communities”
• Inputs to clustering/
segmentation/ profiling
• Biological networks
(health care, genomics,
etc.)
• Predictive analytics (e.g.,
predicting improvements
in recipes based on
ingredient networks)
• Sociology/Economics/
Political Science/etc.
• Computer networks

Kinds of Questions SNA Addresses

Kinds Of Questions that
SNA/NA Address
• How do networks form and grow?
– Compare real-world networks (e.g., the Internet,
Facebook, biological networks) with various
theoretical models
• Do the theoretical models help explain the behavior and growth
dynamics of the real network?
• Example: Randomly-formed network vs. “preferential
attachment”

SNA/NA Address (2)
• How does network structure (topology) affect the
way that information disseminates -- or that
infections spread???

SNA/NA Address (3)
• Based on the number, strength, directionality, and/or
characteristics/attributes of “links,” … and
characteristics of individuals/nodes …
… how do we identify (and characterize)
communities???

Quick Look at SNA/NA Data

What are networks?
• Networks are sets of nodes connected by edges.
“Network” ≡ “Graph”
points lines
vertices edges, arcs math
nodes links computer science
sites bonds physics
actors ties, relations sociology
node
edge

Network elements: edges
• Directed (also called arcs, links)
– A -> B
• A likes B, A gave a gift to B, A is B’s child
• Undirected
– A <-> B or A – B
• A and B like each other
• A and B are siblings
• A and B are co-authors

Directed networks
Ada
Cora
Louise
Jean
Helen
Martha
Alice
Robin
Marion
Maxine
Lena
Hazel Hilda
Frances
Eva
RuthEdna
Adele
Jane
Anna
Mary
Betty
Ella
Ellen
Laura
Irene
• Girls’ school dormitory dining-table partners, 1st and 2nd choices (Moreno,
The sociometry reader, 1960)

Example Adjacency Matrix
1
2
3
45
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 0 0 0 1
1 1 0 0 0
A =

Graph Data: 2 Tables
(Nodes and Edges)

2 Ways that NA is Different From
Conventional (Frequentist) Statistics
• Non-independence of “edge rows”:
– Example: if I am “linked” to two individuals, it often increases the
probability that they are linked to each other
– Implication: one cannot necessarily use statistical tests based on statistical
independence, normal distribution, etc., to understand statistical
significance
• Exploration of real-world “graphs” by comparing them to various
hypothetical (strawman) models
– A Monte Carlo approach:
• Generate large numbers of graphs based on hypothetical models
• Compare the various characteristic of real world graph to the
distribution of same characteristics of the multiple hypothetical
graphs to test the null hypothesis that the real graph is
significantly different than the hypothetical graphs

A Brief Look at Two Topologies

Erdös-Renyi Random Graph:
Simplest Network Model
• Assumptions
– Nodes connect at random
– Network is undirected
• Key parameters
– Number of nodes N
– Either “p” or “M”
• p = probability that any two nodes share an edge
• M = total number of edges in the graph

What ER Random
Networks Look Like
after spring
layout

Preferential Attachment Networks
• Preferential attachment of growing
networks:
– New nodes prefer to attach to well-
connected nodes over less-well connected
nodes
• Process also known as
– Cumulative advantage
– Rich-get-richer
– Matthew effect

Preferential Growth

A Sample of Network Statistics

Node Statistics
• Node network properties
– From immediate connections
• indegree
how many directed edges (arcs) are incident on a node
• outdegree
how many directed edges (arcs) originate at a node
• degree (in or out)
number of edges incident on a node
– From the entire graph
• Centrality (betweenness, closeness)
outdegree=2
indegree=3
degree=5

Giant Component
• if the largest component encompasses a significant fraction of the graph, it is
called the giant component

average degree
sizeofgiantcomponent “Percolation Threshold”
av deg = 0.99 av deg = 1.18 av deg = 3.96
Percolation threshold: how many edges need
to be added before the giant component
appears?
As the average degree increases to z = 1, a
giant component suddenly appears

Shortest Path – And
Average Shortest Path
• How many hops between two nodes?
• On average, how many hops between each
pair of nodes

Centrality

Nodes are sized by degree, and colored by betweenness.
Betweenness: Example

Closeness Example
YX
Y
X
Y
X
Y
X

Example of Eigenvector Centrality (a
Recursive Measure) in Directed Networks
• PageRank brings order to the Web:
– it's not just the pages that point to you, but how many
pages point to those pages, etc.
– more difficult to artificially inflate centrality with a
recursive definition

Degree Distributions: An Example –
With a Log-Log Distribution
• Sexual
networks:
great variation
in contact
numbers

Small World Networks

NE
MA
Small world phenomenon:
Milgram’s experiment

Ties and Geography
“The geographic movement of the [message] from Nebraska to
Massachusetts is striking. There is a progressive closing in on the target
area as each new person is added to the chain”
S.Milgram ‘The small world problem’, Psychology TodayM 1967
NE
MA

Kleinberg’s geographical small world model
nodes are placed on a lattice and connect to nearest neighbors
additional links placed with:
p(link between u and v) = (distance(u,v))-r
If you set r = 2, you get optimum ability to get
between nodes with minimal jumps!!!!!

Communities

Why Care About Communities?
• Opinion formation and uniformity
 If each node adopts the opinion of the majority
of its neighbors, it is possible to have different
opinions in different cohesive subgroups

Political Blogs

Community Finding
• Social and other networks have a natural community structure
• We want to discover this structure rather than impose a certain
size of community or fix the number of communities
• Without “looking”, can we discover community structure in an
automated way?

Hierarchical clustering
• Process:
– after calculating the “distances”for all pairs of vertices
– start with all n vertices disconnected
– add edges between pairs one by one in order of
decreasing weight
– result: nested components, where one can take a
‘slice’ at any level of the tree

Permuted Adjacency Matrix

Betweenness Clustering
• Successively removing edges of highest betweenness (the bridges, or local
bridges) breaks up the network into separate components

Modularity
• Algorithm
– Start with all vertices as isolates
– Follow a greedy strategy:
• successively join clusters with the greatest increase DQ in modularity
• stop when the maximum possible DQ <= 0 from joining any two
– Successfully used to find community structure in a graph
with > 400,000 nodes with > 2 million edges
• Amazon’s people who bought this also bought that…
– Alternatives to achieving optimum DQ:
• simulated annealing rather than greedy search

Some Interesting Applications of NA

Ingredient Networks

Preso on social network analysis for rtp analytics unconference

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