Prepare for your exams
Get points
Guidelines and tips

Prepare for your exams

Study with the several resources on Docsity

Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips

Sell on Docsity

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents

20 Points

For each uploaded document

Answer questions

5 Points

For each given answer (max 1 per day)

All the ways to get free points

Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study

Go to the blog

Network Analysis: Understanding Connections and Communities in Complex Systems, Slides of Data Communication Systems and Computer Networks

Institute of Company Secretaries of India Data Communication Systems and Computer Networks

Various aspects of network analysis, including structural and community aspects, dynamics, algorithms, and outlook. It covers questions related to the number of connections, clusters, growth, and propagation of phenomena in networks. The document also discusses the use of graphs, adjacency matrices, and bipartite networks to represent and analyze networks.

Typology: Slides

2012/2013

Uploaded on 04/23/2013

saraswathi 🇮🇳

(1)

74 documents

1 / 22

This page cannot be seen from the preview

Don't miss anything!

Network Questions: Structural

1. How many connections does the average node have?

2. Are some nodes more connected than others?

3. Is the entire network connected?

4. On average, how many links are there between nodes?

5. Are there clusters or groupings within which the connections are

particularly strong?

6. What is the best way to characterize a complex network?

7. How can we tell if two networks are “different”?

8. Are there useful ways of classifying or categorizing networks?

Docsity.com

Partial preview of the text

Download Network Analysis: Understanding Connections and Communities in Complex Systems and more Slides Data Communication Systems and Computer Networks in PDF only on Docsity!

Network Questions: Structural

How many connections does the average node have?
Are some nodes more connected than others?
Is the entire network connected?
On average, how many links are there between nodes?
Are there clusters or groupings within which the connections are

particularly strong?

_6. What is the best way to characterize a complex network?

How can we tell if two networks are “different”?
Are there useful ways of classifying or categorizing networks?_

Network Questions: Communities

1. Are there clusters or groupings within which the

connections are particularly strong?

2. What is the best way to discover communities,

especially in large networks?

3. How can we tell if these communities are statistically

significant?

4. What do these clusters tell us in specific applications?

Network Questions: Dynamics on

1. How do diseases/computer viruses/innovations/

rumors/revolutions propagate on networks?

2. What properties of networks are relevant to the answer of

the above question?

3. If you wanted to prevent (or encourage) spread of

something on a network, what should you do?

4. What types of networks are robust to random attack or

failure?

5. What types of networks are robust to directed attack?

6. How are dynamics of and dynamics on coupled?

Network Questions: Algorithms

1. What types of networks are searchable or

navigable?

2. What are good ways to visualize complex

networks?

3. How does google page rank work?

4. If the internet were to double in size, would it

still work?

Network Questions: Outlook

• Advances in available data, computing speed, and

algorithms have made it possible to apply network

analysis to a vast and growing number of phenomena.

This means that there is lots of exciting, novel work being

done.

This work is a mixture of awesome, exploratory,

misleading, irrelevant, relevant, fascinating, ground-

breaking, important, and just plain wrong.

• It is relatively easy to fool oneself into seeing thing

that aren’t there when analyzing networks.

This is the case with almost anything, not just networks.

• For networks, how can we be more careful and

scientific, and not just descriptive and empirical?

Lecture 3:

Mathematics of Networks

CS 765: Complex Networks

Slides are modified from Networks: Theory and Application by Lada Adamic

Network elements: edges

Directed (also called arcs)
- A -> B (E (^) BA)
  - 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
Edge attributes
- weight (e.g. frequency of communication)
- ranking (best friend, second best friend…)
- type (friend, relative, co-worker)
- properties depending on the structure of the rest of the graph: e.g. betweenness
Multiedge: multiple edges between two pair of nodes
Self-edge: from a node to itself

Directed networks

girls’ school dormitory dining-table partners (Moreno, The sociometry reader , 1960)
first and second choices shown

Ada

Cora

Louise

Jean

Helen

Martha

Alice

Robin

Marion

Maxine

Lena

Hazel (^) Hilda

Frances Eva

Edna^ Ruth

Adele

Jane

Anna

Mary

Betty

Ella

Ellen

Laura

Irene

Adjacency matrices

• Representing edges (who is adjacent to

whom) as a matrix

– A ij = 1 if node i has an edge to node j

= 0 if node i does not have an edge to j

– A ii = 0 unless the network has self-loops

If self-loop, A (^) ii =?

– A ij = A ji if the network is undirected,

or if i and j share a reciprocated edge

Example:

A =

Adjacency lists

• Edge list

• Adjacency list

is easier to work with if network is - large - sparse
quickly retrieve all neighbors for a node - 1: - 2: 3 4 - 3: 2 4 - 4: 5 - 5: 1 2

4 5

HyperGraphs

Edges join more than two nodes at a time ( hyperEdge )
Affliation networks
Examples
- Families
- Subnetworks

Can be transformed to a bipartite network

C D

A B

C D

A B

Bipartite (two-mode) networks

• edges occur only between two groups of

nodes, not within those groups

• for example, we may have individuals and

events

– directors and boards of directors

– customers and the items they purchase

– metabolites and the reactions they participate in

going from a bipartite to a one-mode

graph

One mode projection
- two nodes from the first

group are connected if they

link to the same node in the

second group

naturally high occurrence of

cliques

some loss of information
Can use weighted edges to

preserve group occurrences

 Two-mode network

group 1

group 2

Collapsing to a one-mode network

• i and k are linked if they both link to j

• Pij = ∑k Bki Bkj

• P’ = B B

T

– the transpose of a matrix swaps Bxy and Byx

– if B is an n x m matrix, BT^ is an m x n matrix

B = B T^ =

Network Analysis: Understanding Connections and Communities in Complex Systems, Slides of Data Communication Systems and Computer Networks

Related documents

Partial preview of the text

Download Network Analysis: Understanding Connections and Communities in Complex Systems and more Slides Data Communication Systems and Computer Networks in PDF only on Docsity!

Network Questions: Structural

Network Questions: Communities

1. Are there clusters or groupings within which the

connections are particularly strong?

2. What is the best way to discover communities,

especially in large networks?

3. How can we tell if these communities are statistically

significant?

4. What do these clusters tell us in specific applications?

Network Questions: Dynamics on

1. How do diseases/computer viruses/innovations/

rumors/revolutions propagate on networks?

2. What properties of networks are relevant to the answer of

the above question?

3. If you wanted to prevent (or encourage) spread of

something on a network, what should you do?

4. What types of networks are robust to random attack or

failure?

5. What types of networks are robust to directed attack?

6. How are dynamics of and dynamics on coupled?

Network Questions: Algorithms

1. What types of networks are searchable or

navigable?

2. What are good ways to visualize complex

networks?

3. How does google page rank work?

4. If the internet were to double in size, would it

still work?

Network Questions: Outlook

• Advances in available data, computing speed, and

algorithms have made it possible to apply network

analysis to a vast and growing number of phenomena.

done.

misleading, irrelevant, relevant, fascinating, ground-

breaking, important, and just plain wrong.

• It is relatively easy to fool oneself into seeing thing

that aren’t there when analyzing networks.

• For networks, how can we be more careful and

scientific, and not just descriptive and empirical?

Lecture 3:

Mathematics of Networks

Network elements: edges

Directed networks

Adjacency matrices

• Representing edges (who is adjacent to

whom) as a matrix

– A ij = 1 if node i has an edge to node j

= 0 if node i does not have an edge to j

– A ii = 0 unless the network has self-loops

– A ij = A ji if the network is undirected,

or if i and j share a reciprocated edge

Adjacency lists

• Edge list

• Adjacency list

Bipartite (two-mode) networks

• edges occur only between two groups of

nodes, not within those groups

• for example, we may have individuals and

events

– directors and boards of directors

– customers and the items they purchase

– metabolites and the reactions they participate in

group are connected if they

link to the same node in the

second group

cliques

preserve group occurrences

 Two-mode network

Collapsing to a one-mode network

• i and k are linked if they both link to j

• Pij = ∑k Bki Bkj

• P’ = B B

T

– the transpose of a matrix swaps Bxy and Byx

– if B is an n x m matrix, BT^ is an m x n matrix