This reExamples of networks for different activities.

Reference:

Overview: This network is [short description here].

Properties:

• Nodes:
• Edges:
• Directed:
• Weighted:

Domain:

Suggested topics:

Example procedure:

• Fig. 1 in the paper.
• Obscure []
• Project the following questions
• Reveal slide

Reference: Visualign. (2012, May 15). Number of neighbors for world countries. Visualign. https://visualign.org/2011/10/06/number-of-neighbors-for-world-countries/

Overview: This network visualization shows the network of neighbouring countries, each node is a country and shared borders are edges. Only non-island countries are visualized for simplicity. The average number of neighbors is roughly 2.7 and there are 323 such border relationships. There are two main components: One corresponding to Europe, Asia and Africa and one corresponding to the Americas. This network shows that the number of neighbors doesn't just depends on the size of the focal country, but on its neighbors' sizes as well.

Properties:

• Nodes: Countries
• Edges: Shared border
• Directed: False
• Weighted: False

Domain: Geographic

Suggested topics: Degree, planar graph, connectedness

Example procedure:

• Mystery slide:
  • Use the "Border-Connected Countries in Europe, Asia, Africa" figure from the linked webpage.
  • Obscure the title and legend from the slide.
  • Ask the following questions:
    • What network is this?
    • What is the average degree of this network?
• Reveal slide: Reveal the title and legend.
• Context slide: Display a reference to the Visualign webpage. Display an additional figure depicting the world map with each country colored by number of neighbors (Figure titled "WorldMap color-coded by number of neighboring countries"). Can also discuss the implications of including bodies of water on "connectedness".

Reference: Bearman, Peter S., et al. “Chains of Affection: The Structure of Adolescent Romantic and Sexual Networks.” American Journal of Sociology, vol. 110, no. 1, July 2004, pp. 44–91. https://doi.org/10.1086/386272.

Overview: This network comprises 573 students involved in a romantic or sexual relationship with another student at a high school. Circles denote individual students; links represent romantic or sexual relationships. While the relationships are inherently temporal, this is a static graph representation. The network's giant component is displayed, as well as smaller components and counts of small motifs (monogamy, for example). The goal of the study was to examine potential sexual disease transmission in a high school from a network science perspective.

Properties:

• Nodes: Students
• Edges: Sexual/Romantic relationship
• Directed: False
• Weighted: False

Domain: Social

Suggested topics: Components, temporal network, disease transmission

Example procedure:

• Mystery slide:
  • Use Fig. 2 from the referenced paper.
  • Obscure the title and legend from the slide.
  • Ask the following questions:
    • What is this network?
    • Why are there so many disconnected pieces?
    • Why are there very few "loops"?
• Reveal slide: Reveal the title and legend and explain what the network is.
• Context slide: Display a reference to the Bearman paper. Display an additional figure (Fig. 4 from the same paper) depicting the temporal directed network from the same data, showing the possible transmission pathways.

Reference: Ryan, Kerrianne, et al. “The CNS Connectome of a Tadpole Larva of Ciona Intestinalis (L.) Highlights Sidedness in the Brain of a Chordate Sibling.” eLife, vol. 5, Dec. 2016. https://doi.org/10.7554/elife.16962.

Overview: This network is visualized by the connectivity matrix for the complete brain of a Ciona intestinalis (Tadpole) larva. The goal of this study was to look into brain asymmetries using the tiny, dorsal tubular nervous system of the ascidian tadpole larva, Ciona intestinalis. Using Serial section electron microscopy (a technique for creating 3D reconstructions of biological tissues by cutting them into thousands of ultra-thin slices with an ultramicrotome and imaging each section with a high-resolution Electron Microscope), they documented the synaptic connectome of the larva’s 177 CNS neurons, forming 6,618 synapses.

Properties:

• Nodes: Neurons
• Edges: Synapses
• Directed: True
• Weighted: True
• Self-loops: True

Domain: Biological

Suggested topics: Directed networks, weighted networks, self-loops, community structure

Example procedure:

• Mystery slide:
  • Use Fig. 16 from the referenced paper.
  • Obscure the title, legend and the color map label from the slide.
  • Ask the following questions:
    • What is this network?
    • List this network's properties: Is it directed or weighted, and does it have self-loops?
    • Any unique structural properties you notice?
• Reveal slide: Reveal the title, legend, and color map label. Explain what the network represents. The colored bars highlighting groups of rows and columns of the matrix represent brain regions. Discuss the modular structure of this network as visualized by blocks.
• Context slide: Display a reference to the Ryan paper. Talk more about how these data were collected and how representing the brain as a network provides new biological insights (such as brain asymmetry).

Reference: World Cup passing networks. (2019). Nicholas Landry. https://nwlandry.com/portfolio/world_cup.html.

Overview: This network shows the network of passes between players in the France-Belgium FIFA World Cup semifinal game in 2018. This network can help identify key players in the game and can be be essential for creating counter-strategies. Teams can use networks like these to identify their opponent's style of play and modify their own to counter.

Properties:

• Nodes: Soccer players (colored by team and weighted by how many passes they completed)
• Edges: Passes between players, weighted by how many times the players pass to each other
• Directed: False (The edges are actually directed, but the network is represented as undirected.)
• Weighted: True

Domain: Sports

Suggested topics: Temporal/Spatial networks, centrality measures, data-driven sports

Example procedure:

• Mystery slide:
  • Choose a game from the link.
  • Obscure team names and game titles from the network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What are the most important nodes?
    • Are there any differences in the connections between green nodes and orange nodes?
• Reveal slide: Reveal and explain what the network is. Ask if any student saw that particular soccer game.
• Context slide: Show the original webpage with the list of additional networks. We asked additional questions like:
  • What do you think the % possession of each team was?
  • Who do you think won the game?

References:

• Tiago de Paula Peixoto . (n.d.). urban_streets — Urban street networks (2017). https://networks.skewed.de/net/urban_streets
• Crucitti, Paolo, et al. “Centrality Measures in Spatial Networks of Urban Streets.” Physical Review E, vol. 73, no. 3, Mar. 2006. https://doi.org/10.1103/physreve.73.036125.
• Latora, Vito, et al. Complex Networks. Cambridge University Press, 28 Sept. 2017. https://doi.org/10.1017/9781316216002.

Overview: These networks are spatial networks depicting the organization of urban streets as 1-square-mile samples. The Crucitti study looks at self-organization in a city and their results show that planned and self-organized cities belong to two different classes, and they find that self-organized cities exhibit scale-free properties whereas planned cities do not.

Properties:

• Nodes: Intersections
• Edges: Streets
• Directed: False
• Weighted: False

Domain: Geographic

Suggested topics: Self-organization, spatial networks, lattices

Example procedure:

• Mystery slide:
  • Use any of the cities from the link, we used NYC, Cairo, Richmond, and Seoul.
  • We obscured the names of the cities.
  • Ask the following questions:
    • What are these networks?
    • What are the nodes and edges?
    • What do you notice about the structure of these networks?
• Reveal slide: Reveal the city names and explain what the networks represent.
• Context slide: Link the source of the network. We used these networks to introduce the concept of lattices.

Reference: Some temporal network visualizations. (2022, October 26). Petter Holme. https://petterhol.me/2021/06/19/some-temporal-network-visualizations/.

Overview: This video depicts a temporal proximity network of children in a French primary school (ages 6 - 12). Throughout the animation, there are clear transitions between lecture and recess/lunch break as students start to mingle or again separate into separate classrooms.

Properties:

• Nodes: Students (Circles)/Teachers (Squares)
• Edges: Proximity
• Directed: False
• Weighted: True

Domain: Social

Suggested topics: Temporal networks, social ties, influence

Example procedure:

• Mystery slide:
  • Use the animation from the link
  • There isn't any information to obscure.
  • Ask the following questions:
    • What is this network?
    • What are nodes and links?
    • What are the blobs?
    • What network representation choices were made?
    • What do the square vs. circular nodes represent?
• Reveal slide: Reveal and explain what the animation shows.
• Context slide: Link the source of the network.

References:

• Women pioneers II. (2023, November 10). Petter Holme. https://petterhol.me/2023/11/10/women-pioneers-ii/
• Davis, A., Gardner, B. B., & Gardner, M. R. (2022). Deep South: A Social Anthropological Study of Caste and Class. University of Chicago Press.

Overview: We used the "Southern women data" as a an example in our class. This dataset is a record of 18 women observed over a nine-month period. During that period, various subsets of these women met in a series of 14 informal social events. The data recorded which women attended each event. This is a bipartite (or higher-order) network and the attendance log can be thought of as an incidence matrix.

Properties:

• Nodes: Women
• Edges: Attendance at same event
• Directed: False
• Weighted: false

Domain: Social

Suggested topics: Bipartite networks, social ties, influence

Example procedure:

• Mystery slide:
  • Use the "The actual network data from Deep South, collected by Mary Gardner" incidence matrix visualization.
  • Remove any text that identifies the network: the left column (titled "Names of participants in group I"), the caption, and the header (titled "Code numbers and dates...")
  • Ask the following questions:
    • What is this network?
    • What are nodes and what are edges?
    • What is this network representation?
    • How do you think these data were collected?
• Reveal slide: Reveal the obscured data. Talk about which of the women are most and least social.
• Context slide: Reference the Davis book. Introduce the concept of a bipartite network. Highlight how collecting data determines the resulting network. For example, the definition of an "informal social event" changes the events you report and thus, the resulting network.

Reference: Pei, Sen, et al. “Contact Tracing Reveals Community Transmission of COVID-19 in New York City.” Nature Communications, vol. 13, no. 1, Oct. 2022. https://doi.org/10.1038/s41467-022-34130-x.

Overview: This is a self-reported exposure network created at an individual level during COVID-19 tracing in New York City. They sampled 947,042 individuals within 242,486 disjoint clusters. The clusters are color-coded based on the focal individual's home borough. There was considerable diversity in network structures, ranging from hub-and-spoke networks with single spreaders to networks with multiple spreaders. Both within- and cross-borough contacts were recorded. Contact tracing is crucial for understanding the spread of diseases and for deploying interventions to the system.

Properties:

• Nodes: Individuals
• Edges: Secondary infections
• Directed: False/True
• Weighted: False

Domain: Social/Biological

Suggested topics: Interaction networks, disease transmission, intervention strategies.

Example procedure:

• Mystery slide:
  • Use Fig. 2 from the Pei paper.
  • Crop the figure so that only panels (c) and (f) are visible along with the borough color bars.
  • Ask the following questions:
    • What are these networks?
    • What structural characteristics do you notice about each?
• Reveal slide: Reveal all panels. Caption (c) as "The exposure network is undirected. Index cases and reported close contacts are connected." and (f) as "Visualizes transmission clusters with more than six infected individuals."
• Context slide: Reference the Pei paper. We initiated a discussion on the friendship paradox and how it relates to disease spread. How can one use this paradox to design better intervention strategies?

Reference: Sumida Penguins Relationship Chart 2025. (2025). Sumida Aquarium. https://www.sumida-aquarium.com/sokanzu/en/2025/

Overview: This is the interaction network between penguins and zookeepers at the Sumida aquarium in Tokyo, Japan. The network shows the relationships of different types between penguins and their zookeepers.

Properties:

• Nodes: Penguins and zookeepers (Nodes are colored by a zookeeper-determined grouping)
• Edges: Relationship (There are several different types of edges, such as friendship, marriage, cheating, fighting, etc.)
• Directed: True
• Weighted: False (But edges have attributes)

Domain: Social, Multilayer, Cute

Suggested topics: Multilayer networks

Example procedure:

• Mystery slide:
  • Use the Sumida infographic.
  • Obscure the name of the network and the legend.
  • Ask the following questions:
    • What different types of relationships are there?
    • What different types of nodes are there?
    • How was this network collected?
• Reveal slide: Uncover the title and legend. Discuss the different types of edges and nodes.
• Context slide: Share the reference to the Sumida Aquarium page. Display a few close-up subsets of the network and talk about them in greater detail (students really enjoyed talking about the love triangles, unfaithful penguins, and aggressive penguins). Ask the students, How would you represent this network? Use this opportunity to introduce the concept of multilayer (multiplex!) networks.

Reference: Card, Daren C., et al. “Phylogeographic and Population Genetic Analyses Reveal Multiple Species of Boa and Independent Origins of Insular Dwarfism.” Molecular Phylogenetics and Evolution, vol. 102, Sept. 2016, pp. 104–16. https://doi.org/10.1016/j.ympev.2016.05.034.

Overview: This network shows the population structuring and relationships inferred from nuclear RADseq data in Boa constrictor species. The figure shows three major continental clades alongside some intraclade diversity, including two well-supported clades in Central America that each include island populations.

Properties:

• Nodes: Taxonomic unit
• Edges: Inferred descendant
• Directed: False (Though there is inherent direction in ancestry)
• Weighted: False (Though the length is the elapsed time)

Domain: Biological

Suggested topics: Phylogeny, trees

Example procedure:

• Mystery slide:
  • Use Fig. 4 from the Card paper.
  • Obscure the name and legend of this network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and the edges?
    • What are the different colored links?
• Reveal slide: Reveal the name, legend, and species that this tree represents.
• Context slide: Share the reference to the Card paper. We shared some takeaways such as (1) three species-level lineages within Boa (community structure!) were identified, localized roughly to South, Central, and North America, (2) estimated lineage divergence dates were older than previous estimates and signals of admixture exist between major lineages, and (3) evidence for multiple evolutionary origins of island populations of Boa with dwarf phenotypes. We also presented Fig. 1 from the same paper. We emphasized that phylogenetic trees are networks too! Also helpful: discuss that these trees are inferred and are a statistical estimate!

References:

• Quantifying hierarchy and dynamics in US faculty hiring and retention. The Larremore Lab. https://larremorelab.github.io/us-faculty/
• Wapman, K. Hunter, et al. “Quantifying Hierarchy and Dynamics in US Faculty Hiring and Retention.” Nature, vol. 610, no. 7930, Sept. 2022, pp. 120–27. https://doi.org/10.1038/s41586-022-05222-x.

Overview: This network illustrates faculty hires between different universities in the US. Each node is a university and an edge from university A to university B indicates that A has hired faculty who received their PhD from B. The color of these edges indicate if the hire moved down in prestige or moved up in prestige.

Properties:

• Nodes: Universities
• Edges: Faculty hires
• Directed: True (one hires from another)
• Weighted: True (based on the number of hires to and from each university)

Domain: Social, Science of Science

Suggested topics: Centrality, mechanisms (like preferential attachment) that can produce heterogeneous hiring patterns

Example procedure:

• Mystery slide:
  • Use the hiring pattern network from the link.
  • Obscure the name of this network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and the edges?
    • What are the different colored links?
    • What do the numbers indicate?
• Reveal slide: Caption the network with "This network displays the hiring patterns of institutions in the U.S. Nodes are universities and an edge from A to B indicates that A has hired faculty who received their PhD from B. Red indicates that a faculty was hired by a more prestigious institution than their alma mater and blue indicates that a faculty member was hired at a less prestigious university than their alma mater."
• Context slide: Share a reference to the Wapman paper. Share the statistic that "Overall, 80% of all US trained faculty were trained at just 20.4% of universities." Talk about rich-get-richer dynamics.

Reference: Mistry, Dina, et al. “Inferring High-Resolution Human Mixing Patterns for Disease Modeling.” Nature Communications, vol. 12, no. 1, Jan. 2021. https://doi.org/10.1038/s41467-020-20544-y.

Overview: Each heatmap here represents the average contact frequency between an individual of a given age (horizontal axis) and all of their possible contacts (vertical axis). The contacts shown in different panels are for households, schools, and workplaces. These matrices quantify social mixing across age groups and can illustrate family norms across different countries; in India, for example, joint families with individuals of different ages are more common than in the United States, where smaller families comprising couples and children are the norm. The school and workplace networks also give insights into policies or culture of specific countries. In the U.S. and China, child labor laws create the hard cutoff, whereas in India, this threshold is much lower. The school mixing matrices exhibit large differences across the countries, which may indicate differences in the ages of teachers and school children.

Properties:

• Nodes: Age groups
• Edges: Contact frequencies
• Directed: False
• Weighted: True

Domain: Social

Suggested topics: Social contact networks, modularity, assortativity

Example procedure:

• Mystery slide:
  • Use Fig. 2 from the Mistry paper.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • How do countries and cities differ?
    • What do think (a), (b), and (c) represent?
• Reveal slide: Caption panel (a), (b), and (c) "Country", "School", and "Workplace" and add a text box with the text "Each entry $S_{ij}$ is the contact frequency of age $j$ with age $i$. State that nodes are age groups and that edges are contact frequencies.
• Context slide: Reference the Mistry paper. Fig. 2 is a great point of discussion for talking about cultural differences and how they appear in the age-mixing matrices. (What ages tend to associate with each other across countries and settings and why?)

Reference: Andris, Clio, et al. “The Rise of Partisanship and Super-Cooperators in the U.S. House of Representatives.” PLOS ONE, edited by Rodrigo Huerta-Quintanilla, vol. 10, no. 4, Apr. 2015, p. e0123507. https://doi.org/10.1371/journal.pone.0123507.

Overview: This network visualization illustrates the divide between the Republican and Democratic party members from 1949 - 2012. Nodes are the Congress members and edges are voting agreement between two Congress members above a specified threshold. The networks show that over time, strong community structure has emerged in the voting concordance network, caused by fewer cross-party voting agreement.

Properties:

• Nodes: Individuals in the United States Congress (Blue nodes are Democrat and Red nodes are Republican)
• Edges: Agreement on a bill above a certain threshold
• Directed: False
• Weighted: False (While the number of agreements is weighted, the authors threshold this value)

Domain: Social, political

Suggested topics: Community structure

Example procedure:

• Mystery slide:
  • Use Fig. 2 from the paper.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What do you notice about the structure of the network over time?
• Reveal slide: Display a text box stating, "Nodes are Congress members colored by party. Edges are voting agreement between two Congress members above a specified threshold."
• Context slide: Display a reference to the Andris paper. Display figure 1 and talk about potential mechanisms that drive the separation of distributions.

References:

• Berg, Stuart, et al. Sexual Dimorphism in the Complete Connectome of the Drosophila Male Central Nervous System. openRxiv, 9 Oct. 2025. https://doi.org/10.1101/2025.10.09.680999.
• MaleCNS connectome. (2025). https://male-cns.janelia.org/
• NeuPrint Connectome Explorer. (2025). neuPrint. https://neuprint.janelia.org/ (Note: you must log in with a free account to access)

Overview: This adjacency matrix shows the connection between presynaptic and postsynaptic cells in a Drosophila male central nervous system. In this specific figure, they also found communities of neurons which activate each other and might be involved in common functions.

Properties:

• Nodes: Brain regions
• Edges: Activation between brain regions
• Directed: True
• Weighted: True

Domain: Biology

Suggested topics: Neuronal networks, directed and weighted networks

Example procedure:

• Mystery slide:
  • Use the "Male v0.9: Brain Region Connectivity" figure from https://neuprint.janelia.org/.
  • Obscure the name and legend of this network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • Are there weights/self-loops/multiedges?
    • What structure do you notice in this matrix?
• Reveal slide: Display a text box stating that the nodes are brain regions and edges indicate that one brain region activates another brain region.
• Context slide: Display a reference to the Berg paper (with all of the authors listed to make a point) and Fig. 1a from the Berg paper or something similar (The Neuprint homepage has a nice visualization). Explain the significance of the whole brain connectome [This was a many-author paper! Also, the network is 166,691 nodes (neurons) and 25.6M edges (synaptic connections).]

Reference: Soda, Giuseppe, et al. “In the Network of the Conclave: Social Connections and the Making of a Pope.” Social Networks, vol. 83, Oct. 2025, pp. 215–32. https://doi.org/10.1016/j.socnet.2025.07.003.

Overview: This is a network comprising nodes representing cardinals in the Catholic Church, colored according to a cardinal's region of origin and sized proportional to its eigenvector centrality, and edges representing co-membership of collegial bodies and co-consecration. This was one of the few studies predicting Robert Prevost as a potential papal candidate based on his high network centrality.

Properties:

• Nodes: Cardinals
• Edges: Co-membership and consecration ties
• Directed: False
• Weighted: False

Domain: Social, religious

Suggested topics: Predictive networks, centrality measures

Example procedure:

• Mystery slide:
  • Use Fig. A4 from the paper.
  • Obscure the name and legend of this network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What do the colors and sizes indicate?
• Reveal slide: Reveal the name and legend. Describe the co-consecration and co-membership links. This network was used to highlight how networks can be used to make predictions about real-world events.
• Context slide: Display a reference to the Soda paper. Explain the context that network methods successfully predicted the next pope, despite the fact that he was a dark horse candidate. Discuss the fact that higher-order networks were probably a more appropriate choice of a network representation.

Reference: Han, Hye Joo, et al. “The Cognitive Social Network in Dreams: Transitivity, Assortativity, and Giant Component Proportion Are Monotonic.” Cognitive Science, vol. 40, no. 3, May 2015, pp. 671–96. https://doi.org/10.1111/cogs.12244.

Overview: These networks show whether different characters were present together in the dreams of individual dreamers.

Properties:

• Nodes: Characters
• Edges: Co-occurrence in the same dream
• Directed: False
• Weighted: False

Domain: Pychology

Suggested topics: Network representations

Example procedure:

• Mystery slide:
  • Use the top half of Fig. 1 from the Han paper.
  • Obscure the name and legend of this network.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What types of motifs do you notice?
• Reveal slide: Reveal the caption "Social networks of characters in Phil's dreams. Each component is drawn separately." Reveal Alta's dream network. Compare the two and ask, "which person do you think has the richer dream life and why?"
• Context slide: Reference the Han paper. Mention that this network could be (possibly more accurately) represented as a higher-order network. We also summarized major takeaways from the paper:
  • Characters appear in dreams systematically.
  • Waking life social networks tend to have positive assortativity, while in dream social networks, assortativity is often negative or near 0, which could be explained by a random walk.

Reference: Oyarte Galvez, Loreto, et al. “A Travelling-Wave Strategy for Plant–Fungal Trade.” Nature, vol. 639, no. 8053, Feb. 2025, pp. 172–80. https://doi.org/10.1038/s41586-025-08614-x.

Overview: These networks are the plant-fungal trade networks for the mycorrhizal fungi. Fungi construct and use these networks to collect and trade nutrient resources with plant roots. Owing to their dependence on host-derived carbon, these fungi face conflicting trade-offs in building networks that balance construction costs against geographical coverage and long-distance resource transport to and from roots.

Properties:

• Nodes: Fungal nodes
• Edges: Cytoplasmic flow
• Directed: False
• Weighted: False

Domain: Biological, Transportation

Suggested topics:

Example procedure:

• Mystery slide:
  • Use Fig. 1(b) from the Galvez paper.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What happens over time?
• Reveal slide: Reveal panel (a) and describe the network.
• Context slide: Display a reference to the Galvez paper. Display Figs. 2 and 4 for context on the radial propagation of the hyphae and network measures.

Reference: The Star Wars social network. (2015, December 15). Evelina Gabasova’s Blog. https://evelinag.com/blog/2015/12-15-star-wars-social-network/

Overview:

Properties:

• Nodes: Characters in "The Force Awakens"
• Edges: Co-occurrence in a movie scence
• Directed: False
• Weighted: True

Domain: Social

Suggested topics: Centrality, higher-order vs. pairwise

Example procedure:

• Mystery slide:

  • Use "The Force Awakens" figure from the Gabasova webpage.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • What are the most central nodes by degree and betweenness?
    • What would be other appropriate network representations of this system?

• Reveal slide: Caption the network with "The character scene co-occurrences in The Force Awakens". Reveal the centralities of each of the nodes.

• Context slide: Display a reference to the Gabasova webpage. Display the network from the entire cinematic universe from the same webpage.

Reference: Gray, Tyler J., et al. “Hahahahaha, Duuuuude, Yeeessss!: A Two-Parameter Characterization of Stretchable Words and the Dynamics of Mistypings and Misspellings.” PLOS ONE, edited by Lidia Adriana Braunstein, vol. 15, no. 5, May 2020, p. e0232938. https://doi.org/10.1371/journal.pone.0232938.

Overview: "Stretched words" like "hahaha" or "heyyyyyy" are commonly found on social media and their length often exaggerates their meaning. This paper maps stretched words onto trees, where each word is a path from the root of the tree to its leaves. The result is a weighted tree, with links weighted by the frequency of the transition from one letter to the next.

Properties:

• Nodes: Letters
• Edges: Adjacent letters in a word
• Directed: True (Though it is visualized as undirected)
• Weighted: True

Domain: Linguistic, social media

Suggested topics: Trees, Branching processes

Example procedure:

• Mystery slide:
  • Use Fig. 10 from the Gray paper.
  • Ask the following questions:
    • What is this network?
    • What are the nodes and edges?
    • Is this network weighted or directed?
    • What do you notice structurally about this network?
• Reveal slide: We display a caption stating, "The root node represents ‘h’. From there, branching to the left (light gray edge) is equivalent to appending an ‘h’. Branching to the right (dark gray edge) is equivalent to appending an ‘a’. The edge width is logarithmically related to the number of tokens that pass along that edge when spelled out. A few example words are annotated, and their corresponding nodes are denoted with a star."
• Context slide: Display a reference to the Gray paper. Display the table 1 from the Gray paper. Share some takeaways:
  • Authors examined the frequency distributions of ‘stretchable words’ found in roughly 100 billion tweets.
  • Created spelling trees.
  • Introduced two parameters: "balance" and "stretch", related to the statistics of these trees.

• Women pioneers II. (2023, November 10). Petter Holme. https://petterhol.me/2023/11/10/women-pioneers-ii/
• Firsts in network science. (2023, August 12). Petter Holme. https://petterhol.me/2019/04/15/firsts-in-network-science/
• Networks of the day. (2023, November 3). Petter Holme. https://petterhol.me/2023/11/02/networks-of-the-day/
• Sumida Penguins Relationship Chart 2024. (2024). Sumida Aquarium. https://www.sumida-aquarium.com/sokanzu/en/2024/
• Matsliah, Arie, et al. “Codex: Connectome Data Explorer.” Unpublished, 2023, https://doi.org/10.13140/RG.2.2.35928.67844.
• Bansal Lab. (2025). GitHub - bansallab/asnr: Animal Social Networks Repository. GitHub. https://github.com/bansallab/asnr