Global Diffusion via Cascading Invitations: Structure, Growth, and - - PowerPoint PPT Presentation

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Global Diffusion via Cascading Invitations: Structure, Growth, and - - PowerPoint PPT Presentation

Oct 06, 2023 282 likes •933 views

Global Diffusion via Cascading Invitations: Structure, Growth, and Homophily Ashton Anderson Stanford Daniel Huttenlocher, Jon Kleinberg, Jure Leskovec, Mitul Tiwari Cornell Cornell Stanford LinkedIn Friday, May 1, 15 growth via cascading

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Global Diffusion via Cascading Invitations: Structure, Growth, and Homophily

Daniel Huttenlocher, Jon Kleinberg, Jure Leskovec, Mitul Tiwari Stanford Stanford Cornell Cornell Ashton Anderson LinkedIn

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growth via cascading signups

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many successful websites grow by their members inviting non-members to join e.g., Gmail, Facebook, LinkedIn, etc. billions of accounts, huge fraction of all web traffic

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questions

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what types of people transmit to what types of people? how do cascades grow over time? what’s the structure of this growth? (is it “viral”?)

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guest invitations

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LinkedIn: 332M members significant fraction are warm signups largest product diffusion event ever analyzed

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guest invitations

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u v

u invites v and v accepts u’s invitation we construct a graph as follows: and v accepts u’s invitation

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guest invitations

these invitations link together and form cascades

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guest invitations

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every cold signup is the root of a signup cascade and v accepts u’s invitation all non-root nodes are warm signups cascades are trees

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guest invitations

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and v accepts u’s invitation time Text

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  • 1. structure
  • 2. growth
  • 3. homophily

global diffusion via cascading invitations

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cascade structure

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prior work found little evidence of real multi-step, person-to-person diffusion and v accepts u’s invitation vast majority of “diffusion” cascades:

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  • 1. structure
  • 2. growth
  • 3. homophily

global diffusion via cascading invitations

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cascade structure

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is there evidence of “viral transmission” on LI? and v accepts u’s invitation

  • ne way to quantify: how many of the adopters

are far from the root?

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cascade structure

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and v accepts u’s invitation adoptions are much deeper on LI than in previous datasets

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cascade structure

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and v accepts u’s invitation another measure: what fraction of adoptions are accounted for in large/deep cascades? than in previous datasets

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cascade structure

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and v accepts u’s invitation so much more viral transmission that we’re

  • bserving qualitatively different behavior

another measure: what fraction of adoptions are accounted for in large/deep cascades? than in previous datasets

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cascade structure

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and v accepts u’s invitation structural virality of a cascade: rigorous measure to interpolate between broadcast and viral diffusion than in previous datasets broadcast (low SV) viral (high SV)

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cascade structure

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and v accepts u’s invitation important question: what’s the relationship between cascade size and structural virality? than in previous datasets if strongly negative or positive, knowing cascade size tells you mechanism by which it grew if close to 0, cascades grow in structurally different ways

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cascade structure

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and v accepts u’s invitation than in previous datasets prior work: Twitter information cascades correlations range from 0.0 to 0.2

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cascade structure

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and v accepts u’s invitation than in previous datasets

  • ur work: LinkedIn signup cascades

strikingly high correlation: 0.72!

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cascade structure

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and v accepts u’s invitation than in previous datasets LinkedIn signup cascades are qualitatively different than previously studied online diffusion datasets direct evidence of a large-scale, multi-step diffusion process ...in contrast with previous work

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  • 1. structure
  • 2. growth
  • 3. homophily

global diffusion via cascading invitations

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growth dynamics

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and v accepts u’s invitation than in previous datasets information cascades grow and flame out very quickly (think news, etc.) what timescales do LI cascades operate over?

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growth dynamics

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and v accepts u’s invitation than in previous datasets time gap between inviter, invitee signups months and years, not hours!

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growth dynamics

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and v accepts u’s invitation than in previous datasets invites accepted quickly invites sent later LI cascades are extremely persistent

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growth dynamics

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and v accepts u’s invitation than in previous datasets

information cascades grow quickly then stagnate LI cascades are much more persistent: what is the growth trajectory of a LI cascade?

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growth dynamics

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and v accepts u’s invitation than in previous datasets tree growth over time for 1K biggest trees surprisingly linear!

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growth dynamics

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and v accepts u’s invitation than in previous datasets LI signup cascades accruing members at a steady, persistent, constant rate not the “burn through the network” picture of information diffusion

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  • 1. structure
  • 2. growth
  • 3. homophily

global diffusion via cascading invitations

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homophily

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and v accepts u’s invitation than in previous datasets homophily: the tendency for people to associate with others like themselves (“birds of a feather flock together”) extremely rich user-level data: we can now see how diffusion relates to underlying node attributes

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homophily

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and v accepts u’s invitation than in previous datasets we consider all cascades with >= 100 nodes (n > 100K of them) every cascade defines a set of members look at distributions of attributes in individual cascades

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homophily

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and v accepts u’s invitation than in previous datasets within-similarity: probability that two randomly chosen nodes match on attribute between-similarity: probability that a randomly drawn node from group 1 matches on attribute with randomly drawn node from group 2 the difference between the two is a measure of homophily

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homophily

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and v accepts u’s invitation than in previous datasets

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homophily

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and v accepts u’s invitation than in previous datasets extreme homophily on geography significant homophily on industry minimal homophily on engagement, max seniority level, and age

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homophily

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and v accepts u’s invitation than in previous datasets

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homophily

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and v accepts u’s invitation than in previous datasets clearly, there is strong homophily on country but does this cascade homophily follow from the

  • bvious edge homophily?

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homophily

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and v accepts u’s invitation than in previous datasets model edge homophily with a first-order Markov chain

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homophily

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and v accepts u’s invitation than in previous datasets model edge homophily with a first-order Markov chain

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87 BR CA CA FR IN US BR FR IN US

empirically derived transition matrix:

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homophily

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and v accepts u’s invitation than in previous datasets model edge homophily with a first-order Markov chain

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87 BR CA CA FR IN US BR FR IN US

edge homophily

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US US US CA IN US IN US US CA

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US US BR

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US US BR

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US US US BR US BR

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets simulate signup diffusion with first-order Markov chain

US US US BR US BR US US IN BR

0.85 0.01 0.01 0.02 0.11 0.03 0.60 0.06 0.06 0.25 0.02 0.10 0.65 0.03 0.20 0.03 0.02 0.01 0.82 0.12 0.05 0.02 0.01 0.05 0.87

BR CA CA FR IN US BR FR IN US

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homophily

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and v accepts u’s invitation than in previous datasets keep all cascade structures the same run this first-order Markov chain process to generate simulated attribute distributions compute within-similarity as before if distribution over similarities is similar, then cascade homophily follows from edge homophily

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homophily

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and v accepts u’s invitation than in previous datasets Markov-generated similarities much lower than observed values!

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homophily

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and v accepts u’s invitation than in previous datasets this reveals a deep fact: LI signup cascades are not arbitrary sets of members that there is cascade homophily above and beyond the already-high edge homophily means that there is higher-order structure in the cascades

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homophily

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and v accepts u’s invitation than in previous datasets repeat the same experiment with second-order Markov chain instead of considering just the parent, consider grandparent and parent

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homophily

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and v accepts u’s invitation than in previous datasets “second-order effects” very large here

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homophily

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and v accepts u’s invitation than in previous datasets how long-range is the dependence? root-guessing experiment borrowed from genetics given node attributes at depth d, does plurality attribute match root attribute?

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homophily

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and v accepts u’s invitation than in previous datasets

US US US BR US BR US US IN BR US BR

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homophily

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and v accepts u’s invitation than in previous datasets

US US US BR US BR US US IN BR US BR

US US

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homophily

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and v accepts u’s invitation than in previous datasets

US US US BR US BR US US IN BR US BR

US US US

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homophily

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and v accepts u’s invitation than in previous datasets

US US US BR US BR US US IN BR US BR

US US BR US

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homophily

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and v accepts u’s invitation than in previous datasets — real attributes — first-order Markov generated attributes — second-order Markov generated attributes run this experiment on:

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homophily

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and v accepts u’s invitation than in previous datasets

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homophily

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and v accepts u’s invitation than in previous datasets genetic processes are first-order by definition higher-order dependencies in our setting is thus analogous to phenotypes, not genotypes a member profile is like a social phenotype what would a social genotype look like?

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conclusion

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LI cascades much more structurally viral than previously studied diffusion datasets they grow persistently over time significant homophily patterns at cascade level, meaning cascades are coherent sets of members

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thank you!

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status effects

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status effects

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