This document provides supplementary material for an article on an analytical reasoning task that revealed limits of social learning in networks. It includes screenshots of the experimental tutorial and quiz questions. It then lists the questions used, including 3 Cognitive Reflection Test (CRT) questions and 4 Berlin Numeracy Test (BNT) questions. Graphs show response patterns to the BNT questions produced little variance. The document describes the network structures used - Barabasi-Albert, clustered, Erdos-Renyi, and full graph - and provides details on their properties at both the micro and macro levels. Finally, it includes graphs showing the evolution of correct and incorrect answers on different network/question combinations.
Bridging Centrality: Identifying Bridging Nodes in Transportation NetworkEswar Publications
To identify the importance of node of a network, several centralities are used. Majority of these centrality measures are dominated by components' degree due to their nature of looking at networks’ topology. We propose a centrality to identification model, bridging centrality, based on information flow and topological aspects. We apply bridging centrality on real world networks including the transportation network and show that the nodes distinguished by bridging centrality are well located on the connecting positions between highly connected regions. Bridging centrality can discriminate bridging nodes, the nodes with more information flowed through them and locations between highly connected regions, while other centrality measures cannot.
Medicinal Applications of Quantum ComputingbGeniusLLC
Here, I study to understand how computational and mathematical models are used to describe EEG readings of the brain in order to assess if these methods can be expanded into further research efforts to create better antidepressants.
Chapter 10Matching MarketsFrom the book Networks, Crow.docxcravennichole326
Chapter 10
Matching Markets
From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World.
By David Easley and Jon Kleinberg. Cambridge University Press, 2010.
Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/
We have now seen a number of ways of thinking both about network structure and
about the behavior of agents as they interact with each other. A few of our examples have
brought these together directly — such as the issue of tra!c in a network, including Braess’s
Paradox — and in the next few chapters we explore this convergence of network structure
and strategic interaction more fully, and in a range of di"erent settings.
First, we think about markets as a prime example of network-structured interaction
between many agents. When we consider markets creating opportunities for interaction
among buyers and sellers, there is an implicit network encoding the access between these
buyers and sellers. In fact, there are a number of ways of using networks to model interactions
among market participants, and we will discuss several of these models. Later, in Chapter 12
on network exchange theory, we will discuss how market-style interactions become a metaphor
for the broad notion of social exchange, in which the social dynamics within a group can be
modeled by the power imbalances of the interactions within the group’s social network.
10.1 Bipartite Graphs and Perfect Matchings
Matching markets form the first class of models we consider, as the focus of the current
chapter. Matching markets have a long history of study in economics, operations research,
and other areas because they embody, in a very clean and stylized way, a number of basic
principles: the way in which people may have di"erent preferences for di"erent kinds of
goods, the way in which prices can decentralize the allocation of goods to people, and the
way in which such prices can in fact lead to allocations that are socially optimal.
We will introduce these various ingredients gradually, by progressing through a succession
of increasingly rich models. We begin with a setting in which goods will be allocated to people
Draft version: June 10, 2010
277
278 CHAPTER 10. MATCHING MARKETS
Room1
Room2
Room3
Room4
Room5
Vikram
Wendy
Xin
Yoram
Zoe
(a) Bipartite Graph
Room1
Room2
Room3
Room4
Room5
Vikram
Wendy
Xin
Yoram
Zoe
(b) A Perfect Matching
Figure 10.1: (a) An example of a bipartite graph. (b) A perfect matching in this graph,
indicated via the dark edges.
based on preferences, and these preferences will be expressed in network form, but there is
no explicit buying, selling, or price-setting. This first setting will also be a crucial component
of the more complex ones that follow.
Bipartite Graphs. The model we start with is called the bipartite matching problem, and
we can motivate it via the following scenario. Suppose that the administrators of a college
dormitory are ...
Identification system of characters in vehicular platesIJRES Journal
In this paper, is proposed a system that identifies the location and dimensions of the characters
relative to the image of a vehicular plate, when the location of the plate has not been accurate. The system is
divided into 4 stages, each with a specific purpose. Which are: binarization by thresholding, morphological
filtering, identification of the largest area and segmentation similarity. The first stage is used to find at the extent
if possible, the region occupied by the plate relative to the rest of the image. Then, in the filtering step, it seeks
to eliminate as far as possible the noise that interferes with the identification of the characters. The third stage is
used to identify the region occupied by the plate. Finally, in the fourth and last stage the segmentation by
similarity is used to identify position and dimension of the characters in the image, in stage a Kohonen neural
network is used.
When spatial data are distributed across multiple servers, there is an obvious difficulty with computing the likelihood function without combining all the data onto one server. Therefore, it would be of interest to compute estimates of the spatial parameters based on decompositions of the spatial held into blocks, each block corresponding to one server. Two methods suggest themselves, a \between blocks" approach in which each block is reduced to a single observation (or a low dimensional summary) to facilitate calculation of a likelihood across blocks, or a within blocks" approach in which the likelihood is calculated for each block and then combined into an overall likelihood for the full process. In fact, I argue that a hybrid approach that combines both ideas is best. Theoretical calculations are provided for the statistical efficiency of each approach. In conclusion, I will present some thoughts for optimal sampling designs with distributed data.
EVOLUTIONARY CENTRALITY AND MAXIMAL CLIQUES IN MOBILE SOCIAL NETWORKSijcsit
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
ALTERNATIVES TO BETWEENNESS CENTRALITY: A MEASURE OF CORRELATION COEFFICIENTcsandit
In this paper, we measure and analyze the correlation of betweenness centrality (BWC) to five centrality measures, including eigenvector centrality (EVC), degree centrality DEG),
clustering coefficient centrality (CCC), farness centrality (FRC), and closeness centrality(CLC). We simulate the evolution of random networks and small-world networks to test the correlation between BWC and the five measures. Additionally, nine real-world networks are also involved in our present study to further examine the correlation. We find that DEG is
highly correlated to BWC on most cases and can serve as alternative to computationallyexpensive BWC. Moreover, EVC, CLC and FRC are also good candidates to replace BWC on
random networks. Although it is not a perfect correlation for all the real-world networks, there still exists a relatively good correlation between BWC and other three measures (CLC, FRC and EVC) on some networks. Our findings in this paper can help us understand how BWC correlates to other centrality measures and when to decide a good alternative to BWC
Quantum persistent k cores for community detectionColleen Farrelly
PPT overview of paper accepted for 2019 Southeastern International Conference on Combinatorics, Graph Theory & Computing. Details a persistence approach to community detection and a new quantum persistence-based algorithm based on the coloring problem.
A NEW SURVEY ON BICLUSTERING OF MICROARRAY DATAcscpconf
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
Open Signal 2014 Android Fragmentation ReportDario Caliendo
Al pari delle più importanti ricorrenze, arriva puntuale anche quest'anno il rapporto di Open Signal sullo stato di Android, un appuntamento che si rinnova annualmente, con il quale l'azienda specializzata nello studio statistico dei fenomeni relativi alla telefonia mobile rappresenta graficamente l'evoluzione dell'ecosistema del colosso della tecnologia di Mountain View, sempre più diffuso ma caratterizzato da enormi limiti non del tutto negativi.
Con un brevetto depositato nelle scorse ore all'US Patent & Trademark Office, Apple alimenta le speranze di esperti e appassionati di tutto il mondo, che sin dalla sua prima introduzione con l'iPhone 5, attendono l'introduzione di Siri anche su computer.
L'assistente digitale più famoso del mondo arriverà presto in Mac OS X, e a descriverne le funzioni è proprio un brevetto di ben novantadue pagine intitolato “Assistente digitale intelligente in un ambiente desktop". Attivabile tramite una gesture nel trackpad multitouch dei Mac, oppure tramite la frase "Hey Siri", il funzionamento dell'assistente digitale per Mac sarà molto simile a quello già visto su iPhone e iPad, ma oltre alle tipiche possibilità di utilizzo, Siri per Mac analizzerà contestualmente le abitudini dell'utente e apprenderà nuove in maniera del tutto autonoma.
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To identify the importance of node of a network, several centralities are used. Majority of these centrality measures are dominated by components' degree due to their nature of looking at networks’ topology. We propose a centrality to identification model, bridging centrality, based on information flow and topological aspects. We apply bridging centrality on real world networks including the transportation network and show that the nodes distinguished by bridging centrality are well located on the connecting positions between highly connected regions. Bridging centrality can discriminate bridging nodes, the nodes with more information flowed through them and locations between highly connected regions, while other centrality measures cannot.
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Chapter 10Matching MarketsFrom the book Networks, Crow.docxcravennichole326
Chapter 10
Matching Markets
From the book Networks, Crowds, and Markets: Reasoning about a Highly Connected World.
By David Easley and Jon Kleinberg. Cambridge University Press, 2010.
Complete preprint on-line at http://www.cs.cornell.edu/home/kleinber/networks-book/
We have now seen a number of ways of thinking both about network structure and
about the behavior of agents as they interact with each other. A few of our examples have
brought these together directly — such as the issue of tra!c in a network, including Braess’s
Paradox — and in the next few chapters we explore this convergence of network structure
and strategic interaction more fully, and in a range of di"erent settings.
First, we think about markets as a prime example of network-structured interaction
between many agents. When we consider markets creating opportunities for interaction
among buyers and sellers, there is an implicit network encoding the access between these
buyers and sellers. In fact, there are a number of ways of using networks to model interactions
among market participants, and we will discuss several of these models. Later, in Chapter 12
on network exchange theory, we will discuss how market-style interactions become a metaphor
for the broad notion of social exchange, in which the social dynamics within a group can be
modeled by the power imbalances of the interactions within the group’s social network.
10.1 Bipartite Graphs and Perfect Matchings
Matching markets form the first class of models we consider, as the focus of the current
chapter. Matching markets have a long history of study in economics, operations research,
and other areas because they embody, in a very clean and stylized way, a number of basic
principles: the way in which people may have di"erent preferences for di"erent kinds of
goods, the way in which prices can decentralize the allocation of goods to people, and the
way in which such prices can in fact lead to allocations that are socially optimal.
We will introduce these various ingredients gradually, by progressing through a succession
of increasingly rich models. We begin with a setting in which goods will be allocated to people
Draft version: June 10, 2010
277
278 CHAPTER 10. MATCHING MARKETS
Room1
Room2
Room3
Room4
Room5
Vikram
Wendy
Xin
Yoram
Zoe
(a) Bipartite Graph
Room1
Room2
Room3
Room4
Room5
Vikram
Wendy
Xin
Yoram
Zoe
(b) A Perfect Matching
Figure 10.1: (a) An example of a bipartite graph. (b) A perfect matching in this graph,
indicated via the dark edges.
based on preferences, and these preferences will be expressed in network form, but there is
no explicit buying, selling, or price-setting. This first setting will also be a crucial component
of the more complex ones that follow.
Bipartite Graphs. The model we start with is called the bipartite matching problem, and
we can motivate it via the following scenario. Suppose that the administrators of a college
dormitory are ...
Identification system of characters in vehicular platesIJRES Journal
In this paper, is proposed a system that identifies the location and dimensions of the characters
relative to the image of a vehicular plate, when the location of the plate has not been accurate. The system is
divided into 4 stages, each with a specific purpose. Which are: binarization by thresholding, morphological
filtering, identification of the largest area and segmentation similarity. The first stage is used to find at the extent
if possible, the region occupied by the plate relative to the rest of the image. Then, in the filtering step, it seeks
to eliminate as far as possible the noise that interferes with the identification of the characters. The third stage is
used to identify the region occupied by the plate. Finally, in the fourth and last stage the segmentation by
similarity is used to identify position and dimension of the characters in the image, in stage a Kohonen neural
network is used.
When spatial data are distributed across multiple servers, there is an obvious difficulty with computing the likelihood function without combining all the data onto one server. Therefore, it would be of interest to compute estimates of the spatial parameters based on decompositions of the spatial held into blocks, each block corresponding to one server. Two methods suggest themselves, a \between blocks" approach in which each block is reduced to a single observation (or a low dimensional summary) to facilitate calculation of a likelihood across blocks, or a within blocks" approach in which the likelihood is calculated for each block and then combined into an overall likelihood for the full process. In fact, I argue that a hybrid approach that combines both ideas is best. Theoretical calculations are provided for the statistical efficiency of each approach. In conclusion, I will present some thoughts for optimal sampling designs with distributed data.
EVOLUTIONARY CENTRALITY AND MAXIMAL CLIQUES IN MOBILE SOCIAL NETWORKSijcsit
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
ALTERNATIVES TO BETWEENNESS CENTRALITY: A MEASURE OF CORRELATION COEFFICIENTcsandit
In this paper, we measure and analyze the correlation of betweenness centrality (BWC) to five centrality measures, including eigenvector centrality (EVC), degree centrality DEG),
clustering coefficient centrality (CCC), farness centrality (FRC), and closeness centrality(CLC). We simulate the evolution of random networks and small-world networks to test the correlation between BWC and the five measures. Additionally, nine real-world networks are also involved in our present study to further examine the correlation. We find that DEG is
highly correlated to BWC on most cases and can serve as alternative to computationallyexpensive BWC. Moreover, EVC, CLC and FRC are also good candidates to replace BWC on
random networks. Although it is not a perfect correlation for all the real-world networks, there still exists a relatively good correlation between BWC and other three measures (CLC, FRC and EVC) on some networks. Our findings in this paper can help us understand how BWC correlates to other centrality measures and when to decide a good alternative to BWC
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PPT overview of paper accepted for 2019 Southeastern International Conference on Combinatorics, Graph Theory & Computing. Details a persistence approach to community detection and a new quantum persistence-based algorithm based on the coloring problem.
A NEW SURVEY ON BICLUSTERING OF MICROARRAY DATAcscpconf
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
There are subsets of genes that have similar behavior under subsets of conditions, so we say
that they coexpress, but behave independently under other subsets of conditions. Discovering
such coexpressions can be helpful to uncover genomic knowledge such as gene networks or
gene interactions. That is why, it is of utmost importance to make a simultaneous clustering of
genes and conditions to identify clusters of genes that are coexpressed under clusters of
conditions. This type of clustering is called biclustering.
Biclustering is an NP-hard problem. Consequently, heuristic algorithms are typically used to
approximate this problem by finding suboptimal solutions. In this paper, we make a new survey
on biclustering of gene expression data, also called microarray data.
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Al pari delle più importanti ricorrenze, arriva puntuale anche quest'anno il rapporto di Open Signal sullo stato di Android, un appuntamento che si rinnova annualmente, con il quale l'azienda specializzata nello studio statistico dei fenomeni relativi alla telefonia mobile rappresenta graficamente l'evoluzione dell'ecosistema del colosso della tecnologia di Mountain View, sempre più diffuso ma caratterizzato da enormi limiti non del tutto negativi.
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6. A.2
Quiz Questions
Following is the set of quiz questions that participants have to correctly answer before they can proceed to
the experiment. The correct answers are highlighted in bold.
How many times will you see each question?
1. Only once
2. 5 times
Does your reward depends on the responses of other players?
1. Yes
2. No
How do you make money in this game?
1. Every correct response gets me money
2. Not every correct response gets me money, only the last trial counts for each question
3. Not every correct response gets me money, multiple correct responses to the same question only count
as one
6
7. B
Questions
Below is the list of all questions. The first three questions corresponded to the Cognitive Reflection Test
(CRT). These three questions generate an incorrect intuitive answer, which must be inhibited in order to
produce the correct analytic answer [1].
1. [CRT1] In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days
for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?
(Answer: 47)
2. [CRT2] If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to
make 100 widgets? Write the answer in minutes.
(Answer: 5)
3. [CRT3] A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does
the ball cost?
(Answer: 0.05)
After the three CRT questions, subjects moved on to another series of four questions from the Berlin
Numeracy Test (BNT), which we do not discuss in this article [2]. Being either too easy or too hard, these
questions produced little variance between participants in our networks, and thus did not allow us to test
our hypotheses (see Figure 1 below for a visualization of the responses in the BNT questions). As these
question came after participants had completed the three CRT questions, there is no concern that they could
have contaminated the CRT data that we analyze in this article.
1. [BNT1] Imagine we are throwing a five-sided die 50 times. On average, out of these 50 throws how
many times would this five-sided die show an odd number (1, 3 or 5)?
out of 50 throws.
(Answer: 30)
2. [BNT2] Out of 1,000 people in a small town 500 are members of a choir. Out of these 500 members
in the choir 100 are men. Out of the 500 inhabitants that are not in the choir 300 are men. What is
the probability that a randomly drawn man (not a person) is a member of the choir? (please indicate
the probability in percents)
(Answer: 25)
3. [BNT3] Imagine we are throwing a loaded die (6 sides). The probability that the die shows a 6 is
twice as high as the probability of each of the other numbers. On average, out of these 70 throws, how
many times would the die show the number 6?
out of 70 throws.
(Answer: 20)
4. [BNT4] In a forest 20% of mushrooms are red, 50% brown and 30% white. A red mushroom is
poisonous with a probability of 20%. A mushroom that is not red is poisonous with a probability of
5%. What is the probability that a poisonous mushroom in the forest is red?
(Answer: 50)
7
8. Proportion of correct responses
TOPOLOGY
Full
First Question
Erdos−Renyi
Barabasi−Albert
Second Question
Clustered
Third Question
Baseline
Fourth Qestion
1.00
0.75
0.50
0.25
0.00
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
Trial
Figure 1: BNT questions are either too easy or too hard, reducing variance observed in CRT questions.
8
9. C
C.1
Network Structures & Their Properties
The Networks
A network (or graph) consists of a set V vertices (a.k.a. nodes, individuals), and a set E of edges (a.k.a.
connections or links) between them. Elements of E can be denoted by a pair Eij = (i, j) where i, j 2 V .
Each of our experimental sessions ran on one of the four graphs: (1) Barabasi-Albert model; (2) Clustering
graph; (3) Erdos-Renyi model; (4) Full graph. The di↵erent graph structures are visually depicted below.
These graphs were chosen due to significant discrepancy in their measures on the macro (network) and micro
(node) level, as shown below.
Barabasi−Albert model
Clustering graph
Full graph
Erdos−Renyi model
Figure 2: List of graphs
9
10. C.2
Micro Measures
And on the micro level (for each node):
Degree: The degree ki of a vertex i is simply the number of edges incident to this vertex. In a directed
graph, we can distinguish between the out-degree (outgoing edges) and in-degree (incoming edges). In the
present paper, edges are considered undirected.
The di↵erent graph structures we used have significantly varying distributions of node degrees, as shown
below. The degree distribution of the Erdo-Renyi graph follows a Poission distribution, thus most nodes
have a more or less equal number of neighbors (no one is disproportionately popular). In contrasted, in the
Barabasi-Albert graph, the distribution is long-tailed, with a few very highly connected nodes. In the full
graph, everyone has equal degree, since everyone is connected to everyone else. Finally, in the clustering
graph, degrees are more or less identical. However, as we will see below, some nodes are a more privilaged
position in the middle of the graph.
Barabasi model
Erdos−Renyi model
20
20
15
15
10
10
5
5
0
0
5
10
15
0
20
0
Full graph
5
10
15
20
Clustering graph
20
20
15
15
10
10
5
5
0
0
5
10
15
0
20
0
5
10
15
20
Figure 3: Degree distribution
Local clustering coe cient: The local clustering coe cient captures the following intuition: out of all
pairs of friends that i is connected to, how many of those friends are also friends with one another. In other
words:
Ci =
number of triangles connected to node i
number of triples centered around node i
where a triple centred around node i is a set of two edges connected to node i (if the degree of node i is 0
or 1, we which gives us Ci = 0/0, we can set Ci = 0). High local clustering coe cient for node i indicates
that i belongs to a tightly knit group.
More formally, the local clustering coe cient ci is defined as follows:
Ci =
|{Ejk }|
: vj , vk 2 Ni , Ejk 2 E
ki (ki 1)
where ki is the out-degree of vertex i, and Ni = {vj : Eij 2 E} is the set of out-neighbours of vertex i. For
10
11. undirected graphs the value of Ci is normalized as Ci0 = 2Ci . If to rephrase this in the simple words, the
local clustering coe cient of a vertex in a graph shows how close its neighbors are to being a full graph.
The figure below highlights how the distribution of local clustering coe cients varies significantly across
the di↵erent network structures. In particular, nodes in the Erdos-Renyi and Barabasi-Albert graphs have
much lower clustering compared to the Clustering graph. Note that in the full graph, every node has a local
clustering coe cient of 1, since everyone is connected to everyone else.
Betweenness centrality: The betweenness centrality of a node is equal to the number of shortest
paths (among all other vertices) that pass through that node. The higher the number, the more important
is the node, in the sense that there is a small number of hops between that node and the majority of the
network. Mathematically it can be defined as
g(v) =
X
s6=v6=t
st (v)
st
where st is the total number of shortest paths from node s to node t and st (v) is the number of those
paths that pass through v.
The figure below shows that the betweenness centrality of nodes in the Clustering graph vary significantly
(contrast this with the fact that the node degrees in this graph are almost identical to one another).
Clustering coefficient
1
0.5
0
Barabasi model Erdos−Renyi model
Full graph
Clustering graph
Betweenness centrality
60
40
20
0
−20
Barabasi model Erdos−Renyi model
Full graph
Clustering graph
Figure 4: Clustering coe cient, betweenness centrality
C.3
Macro Measures
2|E|
Graph density: In graph theory, graph density is defined as |V |(|V | 1) . Density represents the ratio of
the number of edges to the maximum number of possible edges. Density will therefore have a value in the
interval [0, 1].
Clustering coe cient of a graph: The clustering coe cient of an undirected graph is a measure of the
number of triangles in a graph. The clustering coe cient for the whole graph is the average of the local
clustering coe cients Ci :
n
1X
C=
Ci
n
i=1
11
12. where n is the number of nodes in the network. By definition 0 Ci 1 and 0 C 1.
Diameter: Diameter of the graph is the lenght of the longest shortest path between any two vertices of the
graph.
Macro level parameters for the four classes of networks are summarized in the table below. Note how
the density and diameter of all graphs is almost identical, with the exception of the full graph, which has
maximum density.
graph type
Barabassi
Erdos-Renyi
Full graph
Clustering graph
Density
0.195
0.211
1
0.179
Clustering
0.208
0.158
1
0.714
12
Diameter
4
4
1
5
Number of edges
37
40
190
34
13. D
Evolution of Network States
The figures below show samples of the detailed evolution of correct (blue) and incorrect answers (red) in a
selection of network/question combinations.
Figure 5: Evolution of the game (Barabasi-Albert, question 1)
13
18. References
[1] Frederick S. Cognitive reflection and decision making.
2005;19(4):25–42.
The Journal of Economic Perspectives.
[2] Cokely ET, Galesic M, Schulz E, Ghazal S, Garcia-Retamero R. Measuring risk literacy: The Berlin
numeracy test. Judgment and Decision Making. 2012;7(1):25–47.
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