This document provides an overview of different measures for analyzing social networks, including centrality measures, connectivity and cohesion measures, and roles. It discusses centrality measures like degree, closeness, betweenness, and eigenvector centrality for individual nodes. It also covers whole network measures like degree distribution, density, and centralization. The document describes local connectivity and cohesion measures including reciprocity, triad census, transitivity, and clustering coefficients. It discusses how these measures can be applied and interpreted for one-mode projections of two-mode networks.
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.
A high-level overview of social network analysis using gephi with your exported Facebook friends network. See more network analysis at http://allthingsgraphed.com.
Social Network Analysis Workshop
This talk will be a workshop featuring an overview of basic theory and methods for social network analysis and an introduction to igraph. The first half of the talk will be a discussion of the concepts and the second half will feature code examples and demonstrations.
Igraph is a package in R, Python, and C++ that supports social network analysis and network data visualization.
Ian McCulloh holds joint appointments as a Parson’s Fellow in the Bloomberg School of Public health, a Senior Lecturer in the Whiting School of Engineering and a senior scientist at the Applied Physics Lab, at Johns Hopkins University. His current research is focused on strategic influence in online networks. His most recent papers have been focused on the neuroscience of persuasion and measuring influence in online social media firestorms. He is the author of “Social Network Analysis with Applications” (Wiley: 2013), “Networks Over Time” (Oxford: forthcoming) and has published 48 peer-reviewed papers, primarily in the area of social network analysis. His current applied work is focused on educating soldiers and marines in advanced methods for open source research and data science leadership.
More information about Dr. Ian McCulloh's work can be found at https://ep.jhu.edu/about-us/faculty-directory/1511-ian-mcculloh
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.
A high-level overview of social network analysis using gephi with your exported Facebook friends network. See more network analysis at http://allthingsgraphed.com.
Social Network Analysis Workshop
This talk will be a workshop featuring an overview of basic theory and methods for social network analysis and an introduction to igraph. The first half of the talk will be a discussion of the concepts and the second half will feature code examples and demonstrations.
Igraph is a package in R, Python, and C++ that supports social network analysis and network data visualization.
Ian McCulloh holds joint appointments as a Parson’s Fellow in the Bloomberg School of Public health, a Senior Lecturer in the Whiting School of Engineering and a senior scientist at the Applied Physics Lab, at Johns Hopkins University. His current research is focused on strategic influence in online networks. His most recent papers have been focused on the neuroscience of persuasion and measuring influence in online social media firestorms. He is the author of “Social Network Analysis with Applications” (Wiley: 2013), “Networks Over Time” (Oxford: forthcoming) and has published 48 peer-reviewed papers, primarily in the area of social network analysis. His current applied work is focused on educating soldiers and marines in advanced methods for open source research and data science leadership.
More information about Dr. Ian McCulloh's work can be found at https://ep.jhu.edu/about-us/faculty-directory/1511-ian-mcculloh
Clustering Methods and Community Detection with NetworkX. A slide deck for the NTU Complexity Science Winter School.
For the accompanying iPython Notebook, visit: http://github.com/eflegara/NetStruc
Social Network Analysis power point presentation Ratnesh Shah
Basics of social network analysis,Application and also explain interesting study done by facebook , twitter, youtube and many more social media network ,slide contains some of interesting study to get knowledge about online social network analysis.
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.
R. Zafarani, M. A. Abbasi, and H. Liu, Social Media Mining: An Introduction, Cambridge University Press, 2014.
Free book and slides at http://socialmediamining.info/
Network Visualization guest lecture at #DataVizQMSS at @Columbia / #SNA at PU...Denis Parra Santander
- First version was a guest lecture about Network Visualization in the class "Data Visualization" taught by Dr. Sharon Hsiao in the QMSS program at Columbia University http://www.columbia.edu/~ih2240/dataviz/index.htm
- This updated version was delivered in our class on SNA at PUC Chile in the MPGI master program.
Quick introduction to community detection.
Structural properties of real world networks, definition of "communities", fundamental techniques and evaluation measures.
Network measures used in social network analysis Dragan Gasevic
Definition of measures (diameter, density, degree centrality, in-degree centrality, out-degree centrality, betweenness centrality, closeness centrality) used in social network analysis. The presentation is prepared by Dragan Gasevic for DALMOOC.
Social Media Mining - Chapter 9 (Recommendation in Social Media)SocialMediaMining
R. Zafarani, M. A. Abbasi, and H. Liu, Social Media Mining: An Introduction, Cambridge University Press, 2014.
Free book and slides at http://socialmediamining.info/
Clustering Methods and Community Detection with NetworkX. A slide deck for the NTU Complexity Science Winter School.
For the accompanying iPython Notebook, visit: http://github.com/eflegara/NetStruc
Social Network Analysis power point presentation Ratnesh Shah
Basics of social network analysis,Application and also explain interesting study done by facebook , twitter, youtube and many more social media network ,slide contains some of interesting study to get knowledge about online social network analysis.
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.
R. Zafarani, M. A. Abbasi, and H. Liu, Social Media Mining: An Introduction, Cambridge University Press, 2014.
Free book and slides at http://socialmediamining.info/
Network Visualization guest lecture at #DataVizQMSS at @Columbia / #SNA at PU...Denis Parra Santander
- First version was a guest lecture about Network Visualization in the class "Data Visualization" taught by Dr. Sharon Hsiao in the QMSS program at Columbia University http://www.columbia.edu/~ih2240/dataviz/index.htm
- This updated version was delivered in our class on SNA at PUC Chile in the MPGI master program.
Quick introduction to community detection.
Structural properties of real world networks, definition of "communities", fundamental techniques and evaluation measures.
Network measures used in social network analysis Dragan Gasevic
Definition of measures (diameter, density, degree centrality, in-degree centrality, out-degree centrality, betweenness centrality, closeness centrality) used in social network analysis. The presentation is prepared by Dragan Gasevic for DALMOOC.
Social Media Mining - Chapter 9 (Recommendation in Social Media)SocialMediaMining
R. Zafarani, M. A. Abbasi, and H. Liu, Social Media Mining: An Introduction, Cambridge University Press, 2014.
Free book and slides at http://socialmediamining.info/
More than ever, we need to learn how to harness the power of networks to tackle the complex issues we're facing as a society. Here's a quick guide to the basics of social network analysis.
Interested? Sign up at http://kumu.io
Inferring Peer Centrality in Socially-Informed Peer-to-Peer SystemsNicolas Kourtellis
Social applications implemented on a peer-to-peer (P2P) architecture mine the social graph of their users for improved performance in search, recommendations, resource
sharing and others. In such applications, the social graph that connects their users is distributed on the peer-to-peer system: the traversal of the social graph translates to a socially-informed routing in the peer-to-peer layer.
In this work we introduce the model of a projection graph that is the result of mapping a social graph onto a peer-to-peer network. We analytically formulate the relation between metrics in the social graph and in the projection graph. We focus on three such graph metrics: degree centrality, node betweenness centrality, and edge betweenness centrality. We evaluate experimentally the feasibility of estimating these metrics in the projection graph from the metrics of the social graph. Our experiments on real networks show that when mapping communities of 50-150 users on a peer, there is an optimal organization of the projection graph with respect to degree and node betweenness centrality. In this range, the association between the properties of the social graph and the projection graph is the highest, and thus the properties of the (dynamic) projection graph can be inferred from
the properties of the (slower changing) social graph. We discuss the applicability of our findings to aspects of peer-to-peer systems such as data dissemination, social search, peer vulnerability, and data placement and caching.
Inferring Peer Centrality in Socially-Informed Peer-to-Peer Systems. Nicolas Kourtellis and Adriana Iamnitchi. In Proceedings of 11th IEEE International Conference on Peer-to-Peer Computing (P2P'11), Kyoto, Japan, Aug 2011
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
4. Centrality: Individual Nodes
How can we distinguish “important” actors?
• Centrality:
• Who is at the ‘center’ of the network?
…but what is meant by ‘center’ gets complicated
5.
6. How can we distinguish “important” actors?
Centrality
7. Centrality
• Freeman’s (1979) criteria:
1. Calculated on individuals
2. Normalized by network size to compare across
networks
3. Derive network-level centralization counterpart
14. Centrality
Kornienko et al. 2013:
Test cortisol (stress)
on in-degrees, out-
degrees, and ego-
network density.
Find significantly
higher cortisol for low
out-degree, low and
high popularity
17. Centrality
Closeness: Actors considered important if less
distance to all other actors in the network
• inverse distance of each actor to every other
• Geodesic distance – shortest path between
2 actors
• Measurable within a connected graph or
component where each node is reachable
1
1
),()(
g
j
jiic nndnC
18. Centrality
• Closeness
• Inverse of the sum of distances from actor to
all other actors
• Normalized by graph size to range 0-1
1
1
),()(
g
j
jiic nndnC
)1))((()('
gnCnC iCiC
21. Centrality
• Closeness
• Can be directed – (in-closeness and out-
closeness)
…But:
• Non-linear distortion from taking inverse
• Different non-infinity solutions for
disconnected nodes
• Often not calculated as inverse distance
22. Centrality
• Betweenness
• Actor considered important if controls
information flow or bridges relatively
disconnected portions of the network
• Counts number of paths for actor j where j is
on the shortest path between actors i and k
kj
jkijkiB gngnC /)()(
23. Centrality
• Betweenness - number of paths for actor j where j is
on the shortest path between actors i and k
• Landon et al. 2012:
Network contexts of
physicians sharing
patients (bipartite) find
specialists have greater
betweenness in rural
regions than urban
25. Centrality
• Information Centrality
• Like betweenness, but not restricted to
geodesics; information can probably flow
through paths other than geodesics
Betweenness Information Centrality
26. Low Degree/High Betweenness High Degree/Low Betweenness
(few ties crucial for network flow) (many redundant ties)
Centrality: Comparing Measures
29. Low correlations probably tell you something interesting:
Low
Degree
Low
Closeness
Low
Betweenness
High Degree Embedded in cluster
that is far from the
rest of the network
Ego's connections
are redundant -
communication
bypasses him/her
High Closeness Key player tied to
important
important/active
alters
Probably multiple
paths in the
network, ego is near
many actors, but so
are many others
High
Betweenness
Ego's few ties are
crucial for network
flow
Very rare. Would
mean ego
monopolizes the ties
from a small # of
actors to many others.
Centrality: Individual Nodes – Comparing Measures
30. Centrality
• Power- actors are important if tied to other
important actors
• Bonacich Power Centrality (prestige) –
actors tied to other important actors
1)(),( 1
RRIC
Haas et al. 2010 find adolescents with worse self-rated health
have significantly lower Bonacich centrality in their overall school
network.
32. Centrality
• Eigenvector centrality – similar to Bonacich, but
without beta parameter; ego’s eigenvector centrality
is equal to the sum of the centrality of its alters
• Symmetric/undirected data only
• PageRank – eigenvector centrality for directed data
Google describes this as: “PageRank relies on the uniquely democratic nature of
the web by using its vast link structure as an indicator of an individual page’s
value. In essence, Google interprets a link from page A to page B as a vote, by
page A, for page B. But, Google looks at more than the sheer volume of votes, or
links a page receives; it also analyzes the page that casts the vote. Votes cast by
pages that are themselves “important” weigh more heavily and help to make other
pages ‘important.’”
33. Many More Measures
• Peer Influence based measures (Friedkin and others). Based
on the assumed network autocorrelation model of peer
influence; variant of the eigenvector centrality measures
• Fragmentation centrality – Borgatti’s Key Player - nodes are
central if they can easily break up a network
• Removal Centrality – effect on the rest of the network (for any
given statistic) with the removal of a given node; system-
contribution of a particular actor
34. Many More Measures
• Often multiple measures in analysis
• Ennett et al. 2006: higher betweenness, indegree, reach, Bonacich
Power significantly associated with higher alcohol use for 15 year olds
But…
Multicollinearity (don’t forget theory!)
35. • Rather than considering important individual actors,
describing characteristics of the overall network
• To what extent are the links or is the ‘power’ of a
network concentrated in a few nodes, versus spread
throughout the network?
• Degree Distributions
• Centralization
• Density
Centrality in the Network
36. Whole Network Centrality
• Degree Distribution – frequency distribution of
degree values of actors
• A simple random graph will have a Poisson
degree distribution, so variation from that
suggest non-random processes
37. • Degree Distribution – frequency distribution of
degree values of actors
Whole Network Centrality
40. Whole Network Centrality
• Centralization – extent to which centrality is
concentrated in one/few actors; dispersion of
centrality in graph as a whole (Freeman
centralization)
)]2)(1[(
)()(1
*
gg
nCnC
C
g
i iDD
D
41. • Density – volume of relations in network - number
of ties relative to the number of possible ties
Whole Network Centrality
Density = .09
42. • Density – volume of relations in network - number
of ties relative to the number of possible ties
Guan & Kamo 2016: contagion of friends’ depression
varies with density of high school network (Add Health)
Whole Network Centrality
43. Describing Networks
• Beyond centrality, consider structural arrangements
in combination with attributes:
• Similarity of attributes: typically Homophily –
tendency for actors with similar attributes to be more
likely to be connected
• Assortativity - assortative/disassortative mixing
• Individual attributes: gender, same firm
• Structural attributes: same degree
• Descriptive, not distinguishing selection/influence
45. Connecting Measures to Mechanisms: Structural Holes
• Structural holes: absence of ties between alters
• Bridging structural holes: connecting people who
otherwise would not be connected; social capital,
access to resources
• Redundancy (ties that connect ego to alters already
connected to) introduces constraint
• Power, brokerage by controlling info or resources by
bridging structural holes (Simmel’s tertius gaudens)
(Burt 1992)
46. Connecting Measures to Mechanisms: Structural Holes
• 4 related network features:
• Effective Size – (size – redundancy) – average degree of
ego network without counting alters’ ties to ego
• Efficiency – (effective size / observed size)
• Constraint – room to exploit structural holes or negotiate;
extent to which network alters are connected with each
other (direct/indirect, proportion of network ‘time & energy)
• Hierarchy – for Burt/structural holes, many measures of
hierarchy generally – extent to which constraint is
concentrated in one actor
48. Two-Mode Network Data
• Affiliation/Bipartite Network: 2 sets of nodes, with
between-set ties and no within-set ties
Davis’ 1941 ‘Southern
women” dataset (that
we’ll use in lab) shows
women attending social
events
• “Duality of persons and groups”
(Brieger 1974)
49. Two-Mode to One-Mode Network
• One-Mode Projection: Joint connection through opposite
set of nodes becomes the connecting edges
51. Centrality in One-Mode Projections
• Potential bias:
• Projection inflates edges
• Tendency toward cliques, which leads to high density,
clustering coefficients, betweenness, and other measures
• Opaque interpretation
• Solutions:
• Consider order or relative, not absolute, values
• Re-normalize centrality measures (e.g., divide the centrality
measure by the number of degrees in opposite set)
For more information: (Everett 2016; Faust 1997; Jasny 2012; Latapy et al. 2008; Opsahl 2013)
52. Centrality in One-Mode Projections
Pettey et al. 2016 analyze Veterans’ medical visit codes to examine co-
incidence of homelessness and health co-morbidities.
53. Pettey et al. 2016: Co-morbid diagnoses among Veterans
59. Connectivity & Cohesion: Local Processes
• Characterize non-random social patterns in triad
connections with the triad census – counting
observed triads of each possible type
• Transitivity
• If i j and j k, then i k
• With directed ties, observe transitive,
intransitive, vacuous triads
61. Connectivity & Cohesion: Local Processes
• Extending to a network level:
• Comparing triad census to expectation by chance
• Clustering coefficient:
– Transitivity ratio - # closed triads/total # triads
Verdery et al. 2017 – comparing two Respondent Driven Sampling
networks of persons who inject drugs in Philippines; see higher
clustering is associated with higher and faster spread of HIV/AIDS
62. Connectivity & Cohesion: Local Processes
• Social Balance Theory: like nodes, edges can have
attributes, too:
my friend’s friend is my friend,
my friend’s enemy is my enemy,
my enemy’s friend is my enemy,
my enemy’s enemy is my friend Heider (1958)
+
+
+ - -
-
- -
-
64. Connectivity & Cohesion: Clustering
Getting less local:
How can we describe the connective or cohesive
nature of a network overall?
65. Connectivity & Cohesion: Clustering
• Scale-free networks:
• Locally: high-degree nodes act as hubs
– Preferential Attachment
• Globally: networks with highly skewed degree
distributions
• Scale-free implications for diffusion
– Ex: disease transmission via high-degree ‘hubs’
• Often social constraints and patterns mean we
don’t usually see the full scale-free structure
66. Connectivity & Cohesion: Clustering
• Small world graphs:
generally large, sparse,
decentralized, highly
clustered
(Watts & Strogatz, 1998)
• ‘Small World’ phenomenon:
What’s the probability two nodes are connected?
67. Connectivity & Cohesion: Clustering
• Small local changes can have
big effects on the global
network
(Watts & Strogatz, 1998)
• A ‘small world graph’ has relatively small average
path lengths and relatively large clusters
68. Connectivity & Cohesion: Clustering
• Small world graphs:
• ‘shortcuts’ between
clusters dramatically
reduce average path
length
• Can dramatically affect
capacity for disease
transmission or other
network features
69. Connectivity & Cohesion: Clustering
• How else can we measure the ‘small wordliness’ or
other cohesive characteristics of a network?
• Clustering coefficient:
• Average local density (ego-network density/n)
• Transitivity
70. Connectivity & Cohesion: Structural Cohesion
• Structural Cohesion – extent to which networks or
sub-groups within networks are ‘sticky’,
interconnected, or resistant to disruption
• Challenging to measure
• Connectedness maintained through one or a few
actors
• More paths linking network that don’t rely on
one actor = more cohesive
71. Connectivity & Cohesion: Structural Cohesion
• Reachability – actors i and j are reachable if any path in
the network connects them; more paths linking (and re-linking
actors in the group) increases the ability of the group to ‘hold
together’
• Pattern of ties, not just density
D = . 25 D = . 25
72. Node Connectivity
0 1 2 3
Same volume of ties, but graph on right has more independent
paths connecting network, making it more cohesive
Connectivity & Cohesion: Structural Cohesion
73. Connectivity & Cohesion: Components
• Component – maximal connected sub-graph -
connected graph where there is a path between
every node
• Cut-point – node whose removal would
disconnect the graph
• Cut-set – set of nodes necessary for keeping
graph connected
1
2
5
4 3
6
8
7
74. Connectivity & Cohesion: Components
• Formally defining structural cohesion:
1. Minimum number of actors, who if removed,
would disconnect the group
2. Minimum number of independent paths linking
each pair of actors in the group
1
2
5
4 3
6
8
7
76. Connectivity & Cohesion: Components
• Features of components:
• k-components – maximal subset of actors linked
by at least k node-independent paths
• Every member must have at least k ties (but having k
ties doesn’t necessarily make a component)
• 2 k-components can only overlap by k-1 members (or
would be same component)
• Can be nested
77. Connectivity & Cohesion: Components
• Embeddedness – identify cohesive groups
(blocks) in a network, then remove k-cutsets identify
successively deeper embedded groups in graph
Moody & White 2003
78. Connectivity & Cohesion: Groups
• Different types of sub-structures in networks:
• Cliques – all members connected to all other
members
• n-clique – where n is number of steps greater than
direct tie, so can consider 2-clique, defined by 2-step
(friend of a friend) ties
• k-plex – every member to connected to at least n-k
others in the graph (relaxed from connected to all but
self, n-1, of the clique)
• Mostly intractable in large networks
79. Connectivity & Cohesion: Groups
• Different types of sub-structures in networks:
• n-clans – members connected at distance n or
less, only through other members
• k-cores – members joined to at least k other
members, even if not connected to all other
members
81. Roles & Positions: Overall
• Measures that describe subsets
of actors/nodes who have
similarly structured relations
• Might expect different risks or
behaviors for actors occupying
similar positions or roles
82. Roles & Positions: Structural Equivalence
• Structural Equivalence:
• Actors are equivalent if they have the same ties to
the exact same people in the network
• Rare, maybe more restrictive than you want for
thinking about roles and positions in a network,
so can relax to:
• Regular Equivalence:
• Actors are equivalent if have ties to same types
(but not necessarily the exact same) of alters
83.
84. Roles & Positions: Structural Equivalence & Blockmodeling
• Blockmodeling – process of identifying similar positions
(groups of similar actors in a ‘block’ of the adjacency matrix)
• Based on attributes
• Based on patterns of ties
• Can be increasingly generalized and abstracted
• Ex: Core/periphery
1 2
3
85. Roles & Positions: Structural Equivalence
• Structural (Regular) Equivalence: Actors are
equivalent if have ties to same types (but not
necessarily the exact same) of alters
Fujimoto & Valente 2012: Exposure to substance use
through structural equivalence is a better predictor of
drinking and smoking (being connected to the same types
of peers with the same types of behaviors matters more)
than traditional measures of cohesion.
86. In Summary
• Many ways of describing networks or characterizing
nodes of interest within them
• Here: individual node properties, entire network
counterparts, then structures and sub-groups:
• Centrality
• Connectivity & Cohesion
• Roles
• Frame as micro/meso/macro
• Micro: individual nodes
• Meso: sub-groups, sub-graph structures, roles
• Macro: features of entire networks
87. Describing Networks: Summary
• Not considered here:
• Dynamics – churn or stability over time, effects of
changes, etc.
• More 2-mode network methods
• Many more challenging concepts and additions in
describing networks:
• Centrality or structural measures specific to
certain topics or processes
• Groups & Community Detection
89. Resources
Barabasi, A., and Albert, R. (1999). “Emergence of Scaling in Random Networks”. Science 286:5439, 509-512.
Burt, Ronald. (1992). Structural holes: The social structure of competition. Cambridge: Harvard.
Borgatti, Stephen P. 2005. “Centrality and Network Flow.” Social Networks 27 (April 2002): 55–71.
https://doi.org/10.1016/j.socnet.2004.11.008.
Breiger, R. L. (1974). The duality of persons and groups. Social forces, 53(2), 181-190.
Cornwell, B. (2009). Good health and the bridging of structural holes. Social Networks, 31(1): 92-103.
Davis, A., Gardner, B. B. and M. R. Gardner (1941) Deep South, Chicago: The University of Chicago Press.
Ennett, S. T., Bauman, K. E., Hussong, A., Faris, R., Foshee, V. A., Cai, L., & DuRant, R. (2006). The Peer Context of Adolescent
Substance Use: Findings from Social Network Analysis. Journal of Research on Adolescence, 16(2), 159–186.
Everett, M. G. (2016). Centrality and the dual-projection approach for two-mode social network data. Methodological Innovations.
https://doi.org/10.1177/2059799116630662
Faust, K. (1997). Centrality in affiliation networks. Social networks, 19(2), 157-191.
Freeman, L. C. (1979). Centrality in communication networks: Conceptual clarification. Social Networks, 2(2), 119-141.
Fujimoto, K., Chou, C. P., & Valente, T. W. (2011). The network autocorrelation model using two-mode data: Affiliation exposure and
potential bias in the autocorrelation parameter. Social networks, 33(3), 231-243.
Fujimoto, K., & Valente, T. W. (2012). Social network influences on adolescent substance use: Disentangling structural equivalence
from cohesion. Social Science and Medicine, 74(12), 1952–1960.
Granovetter, Mark S.(1973). “The Strength of Weak Ties.” The American Journal of Sociology 78 (6): 1360–80.
Guan, W., & Kamo, Y. (2016). Contextualizing Depressive Contagion: A Multilevel Network Approach. Society and Mental Health,
6(2), 129–145. http://doi.org/10.1177/2156869315619657
Haas, S. A., D. R Schaefer, and O. Kornienko. 2010. “Health and the Structure of Adolescent Social Networks.” Journal of Health
and Social Behavior 51 (4): 424–39. https://doi.org/10.1177/0022146510386791.
Hawe P, Webster C, Shiell A. A glossary of terms for navigating the field of social network analysis. Journal of Epidemiology &
Community Health 2004;58:971-975.
Holland, Paul W., and Samuel Leinhardt. 1976. “Local Structure in Social Networks.” Sociological Methodology 7: 1–45.
Kornienko, O., Clemans, K. H., Out, D., & Granger, D. A. (2013). Friendship network position and salivary cortisol levels. Social
Neuroscience, 8(4), 385–96.
Jasny, Lorien. 2012. “Baseline Models for Two-Mode Social Network Data.” Policy Studies Journal 40 (3): 458–91.
https://doi.org/10.1111/j.1541-0072.2012.00461.x.
Jasny, L. Descriptive Measures for Social Network Analysis, Advanced Networks II seminar slides, ICPSR 2016.
90. Resources, Cont.
Landon, B. E., Keating, N. L., Barnett, M. L., Onnela, J.-P., Paul, S., O’Malley, A. J., … Christakis, N. A. (2012). Variation in Patient-
Sharing Networks of Physicians Across the United States. JAMA: The Journal of the American Medical Association,
308(3), 265.
Latapy, M., Magnien, C., & Del Vecchio, N. (2008). Basic notions for the analysis of large two-mode networks. Social networks,
30(1), 31-48.
Luke, D. A. & J. K. Harris. Network Analysis in Public Health: History, Methods, and Applications. 2007. Annual Review of Public
Health. 28:69-93.
Milgram, S. (1967). The small world problem. Psychology today, 2(1), 60-67.
Moody, J. Slides from Social Networks Seminar, Duke, Spring 2015.
Moody, J., & White, D., (2003). Structural Cohesion and Embeddedness: A Hierarchical Concept of Social Groups. American
Sociological Review, 68: 103-127.
Morris, M., & Kretzschmar, M. (1995). Concurrent partnerships and transmission dynamics in networks. Social Networks, 17(3–4),
299–318
O’Malley, A. J. & P. V. Marsden Health Serv Outcomes Res Methodol. 2008 Dec 1; 8(4): 222–269.
Opsahl, T., 2013. Triadic closure in two-mode networks: Redefining the global and local clustering coefficients. Social Networks 35,
doi:10.1016/j.socnet.2011.07.001
Pettey, W. B., Toth, D. J., Redd, A., Carter, M. E., Samore, M. H., & Gundlapalli, A. V. (2016). Using network projections to explore
co-incidence and context in large clinical datasets: Application to homelessness among US Veterans. Journal of
biomedical informatics, 61, 203-213.
Simmel, Georg. 1950. The Sociology of Georg Simmel. New York: The Free Press.
Schoch, David. “Periodic Table of Centrality Indices”. http://schochastics.net/post/periodic_table/
Scott, J. Social Network Analysis. 2012. SAGE.
Scott, J. & P. J. Carrington. The SAGE Handbook of Social Network Analysis. 2011.
Taheri, S.M., Mahyar, H., Firouzi, M. et al. Soc. Netw. Anal. Min. (2017) 7: 22. https://doi.org/10.1007/s13278-017-0440-7
Valente, T. Social Networks and Health. 2010. Oxford University Press
Verdery, A. M., Siripong, N., & Pence, B. W. (2017). Social network clustering and the spread of HIV/AIDS among persons who
inject drugs in 2 cities in the Philippines. JAIDS Journal of Acquired Immune Deficiency Syndromes, 76(1), 26-32.
Wasserman, S. & K. Faust. Social Network Analysis: Methods and Applications,. 1994 Cambridge.
Watts, D., Strogatz, S.H. (1998). “Collective Dynamics of ‘small-world’ Networks”. Nature 393, 440-442.