🕹 I am Insta Famous

Am I a virus?

Networks
Structure and Processes on Networks
Degree, Power
Network Effects
Published

January 4, 2024

Modified

July 19, 2026

Petr Slováček on Unsplash

Introduction

Do you think your friends have more friends than you have? Do you think that you are outside the herd, and that what you think or do is from your own mind?

How can you possibly be friends with someone who does not say anyways or my bad…

Activities

Activity-1: Secret Santa Game

Let us play this in the vanilla way: Paper chits with names in a bin and drawing them in turn. What can go wrong with this? Ask Avni Gupta.

Should we use this instead? https://www.drawnames.com.sg/secret-santa-generator

Discussion: Nodes, Links, Link Directionality, Connected and Disconnected Networks

Activity-2: Barabasi Cocktail Party Game

This is a game “invented” by Alberto-Laszlo Barabasi, a Network Science pioneer and expert, who has written a wonderful, and wonderfully accessible, book on Network Science, available online. http://networksciencebook.com/

  1. Please take a coin in your hand. (A rupee coin is good!)
  2. Find a stranger potential new friend in the classroom. Both of you toss your coins.
    • Regime #1: If the coins show exactly two Heads, introduce yourselves, make small talk, exchange classroom and college gossip. 2 Minutes!
    • Regime #2: If the coins show two Heads or two Tails, introduce yourselves, make small talk, exchange classroom and college gossip. 2 Minutes!
  4. Make a note of your new friends initials. (“AV”)
  5. We will plot this conversation on the board. How?
Connect the Dots

Discussion: Random Network Mechanisms, Information Flow, Giant Component, Emergence

Activity-3: Indian Surnames Game

  1. How many common Indian surnames do we know? Let us write them on the board.
  2. Each of us will now look at each surname and recollect how many people they know with that surname.
  3. Write down the score for each surname.
  4. Let’s plot this on (yet another) network!!
  5. AND: let us plot a count of tallies for each one of us, and see who knows the most number of surnamed-people! 😹

Discussion: Node Degree, Degree Distribution, Heavy Tail/Scale Free, (Network) Configuration Model

Standard Erdős–Rényi random graphs produce Poisson degree distributions (most nodes have similar degrees, few extremes). Real-world networks are often heavy-tailed (scale-free), with many low-degree nodes and a few high-degree hubs.

Activity-4: Hi, I am Kevin Bacon, SMI Foundation Batch

Let us find a Keven Bacon in SMI Foundation Studies Programme!! Six Degrees of Separation…or of Kevin Bacon? Look at this video before you proceed!

Six Degrees of Separation
  1. Collect friends Data from across college/class, import and plot, analyze and comment
  2. Use this online tool at DataBasic.io https://databasic.io to Connect the Dots, OR
  3. Even more fun at at GraphCommons https://graphcommons.com/graphs/new

Discussion: Node Degree, Centrality, Betweenness, Link Values or Costs

Activity-5: Can you introduce me to Chandler, again?

  1. Take your favourite Literary Work / TV Serial / Movie and create a Network Database for it.
  2. How? Use conversations between pairs of individuals (nodes) to create links. E.g. each distinct conversation is a link, and the number of sentences uttered is the weight of the link.
  3. Visualize it either with or without tech tools From Teach Engineering, this Activity Sheet: https://www.teachengineering.org/activities/view/uno_graphtheory_lesson01_activity2. Hah! Doing Engineering in a Design college!!🤣🤣🤣
  4. Can also use Graph Comicshttps://aviz.fr/~bbach/graphcomics/

Discussion:Everything's Connected ("Old Srishti Proverb." Bah!), Networks are everywhere, You are a node and you are a link...are you?

References

  1. Albert-Laszlo Barabasi. Network Science. http://networksciencebook.com
  2. David Easley and Jon Kleinberg. Networks, Crowds, and Markets:Reasoning About a Highly Connected World. https://www.cs.cornell.edu/home/kleinber/networks-book/
  3. Dmitry Zinoniev. Network Science Intro Slides. https://www.slideshare.net/DmitryZinoviev/workshop-20212296
  4. The Network Effects Bible. https://www.nfx.com/post/network-effects-bible
  5. NetSciEd: Network Literacy: Essential Concepts and Core Ideas. https://sites.google.com/a/binghamton.edu/netscied/teaching-learning/network-concepts
  6. The Historical Network Research Community. https://historicalnetworkresearch.org
  7. Konrad M. Lawson, Toilers and Gangsters: Simple Network Visualization with R for Historians
  8. Frigyes Karinthy. Chains. Read PDF. A Network oriented short story.
  9. Who told you about Srishti? Where? Mark Granovetter, The Strength of Weak Ties, https://www.cs.cmu.edu/~jure/pub/papers/granovetter73ties.pdf
  10. Michele Coscia. 2019. Who will Cluster the Cluster Makers? https://www.michelecoscia.com/?p=1709 Accessed 12 Jan 2024.
  11. Ran Katzir. Nov 16, 2019. Experience Network Science Through Play.https://medium.com/@ran_katzir/teaching-network-science-using-board-games-f78489a3b3bd
  12. Mark Hoffman, Methods for Network Analysis. https://bookdown.org/markhoff/social_network_analysis/
  13. Omar Lizardo and Isaac Jilbert, Social Networks: An Introduction. https://bookdown.org/omarlizardo/_main/

Appendix

“Definitions” of some Network Terms:

Term Definition Example
Network A set of connected nodes and edges. A group of friends on a social media platform forms a network.
Node A vertex or entity in the network. Each friend in that network is a node.
Edge A connection between two nodes. A friendship between two friends is an edge.
Directed Edge An edge that has a direction, indicating a one-way relationship. If A follows B on social media, but B does not follow A back, the edge from A to B is directed.
Weighted Edge An edge that has a weight or value associated with it, representing the strength or capacity of the connection. If A and B communicate frequently, their edge might have a higher weight than an edge between A and C, who rarely communicate.
Path A sequence of edges connecting two nodes. If A is friends with B, and B is friends with C, then A-B-C is a path from A to C.
Connected or Disconnected Network A connected network is one in which there is (atleast one) path between every pair of nodes, while a disconnected network has at least one pair of nodes with no path between them. If every friend in a social media group can reach every other friend through some chain of friendships, the network is connected. If there are isolated friends who cannot reach others, the network is disconnected.
Path length The number of edges along a path between two nodes. If A is connected to B and B to C, the path length from A to C is 2.
Degree The number of edges attached to a node. If one person has 5 friends, their degree is 5.
Betweenness How often a node lies on shortest paths between other nodes. A student who connects two otherwise separate friend groups has high betweenness.
Closeness How near a node is to all other nodes, based on shortest-path distance. A person who can reach everyone else through few steps has high closeness.
Community A group of nodes more densely connected to each other than to the rest of the network. A tightly connected group of classmates is a community.
Characteristic path length The average shortest-path distance across all pairs of nodes. If most people in the network can reach each other in about 3 steps, the characteristic path length is about 3.
Shortest Path The path between two nodes that has the fewest edges. If A is connected to C via B, and also via D *and E, then the shortest path from A to C is A-B-C.
Diameter The longest shortest route between any two nodes in the network. In a small network, the diameter is the longest shortest route between any two people.
Eulerian Path A path that visits every edge in the network exactly once. A mail carrier delivering mail along each street without retracing any street has an Eulerian path.
Hamiltonian Path A path that visits every node in the network exactly once. A traveling salesman visiting each city exactly once has a Hamiltonian path.
Degree distribution The distribution showing how many nodes in a network have degree 1, 2, 3, and so on. The degree of a node is the number of connections it has wikipedia+1. In a friendship network, if most people have 5–10 friends and a few have 100+, the degree distribution summarizes that pattern wikipedia+1.
Power law A pattern where small values are very common and large values are rare, often written as \(P(k)∼k−γP(k) \sim k^{-\gamma}P(k)∼k−γ\) . A network where a few nodes have extremely many links and most have very few links can show a power-law degree distribution wikipedia+1.
Erdős-Rényi network A random network model where each possible edge is included independently with the same probability \(p\). If you generate a graph with 100 nodes and connect each pair with probability 0.05, that is an Erdős-Rényi network.

Fun Stuff

George Cluny and Vera Farmiga embark on a Hamiltonian Trip across the US in (Up in the Air, 2009). The movie is a great example of a Hamiltonian Path. The movie is also a great example of a “Small World” network, where the two characters meet and interact with many people across the US, forming connections and relationships along the way.

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