Measurement and Evolution of Online Social Networks Review of paper by Ophir Gaathon Analysis of Social Information Networks COMS , Spring 2011, Topic #1: April 7th Columbia University Focus Leskovec et al. Graphs over time: densification laws, shrinking diameters and possible explanations.(2005) Space Mislove et al. Measurement and analysis of online social networks. (2007) Leskovec et al. Microscopic evolution of social networks (2008) Kumar et al. Structure and evolution of online social networks. (2010)

Friends of Friends There are different forms/contexts/spheres of interaction on different platforms/networks What are the rules of interaction that every network has? What are the risk and rewords for linking or disconnecting in any given network? Life Work Co-Workers Family Friends of Friends Anonymous What is a social interaction? Online space

What kind of social interaction platform is ? Facebook Linkedin Twiter Flickr youtube

Percent of global Internet users who visit the site * Google as a weekday signal

The Rules Youtube, flickr – ‘just post it’ Facebook – befriend me Twitter- I follow you; you follow me (according to center of gravity) Scientific Papers – you must reference prior work Patents – you must identify prior art

How do real graphs evolve over time? What are “normal” growth patterns in social, technological, and information networks? (A) Constant average degree assumption: The average node degree in the network remains constant over time. (Or equivalently, the number of edges grows linearly in the number of nodes.) (B) Slowly growing diameter assumption: The diameter is a slowly growing function of the network size, as in “small world” graphs. (A’) Empirical observation: Densification power laws: The networks are becoming denser over time, with the average degree increasing (and hence with the number of edges growing super- linearly in the number of nodes). Moreover, the densification follows a power-law pattern. (B’) Empirical observation: Shrinking diameters: The effective diameter is, in many cases, actually decreasing as the network grows.

arXiv started in 1991 as a repository for preprints in physics and later expanded to include astronomy, mathematics, computer science, nonlinear science, quantitative biology and, most recently, statistics.[2].repositorynonlinearbiology[2] In many fields of mathematics and physics, almost all scientific papers are placed on the arXiv. On October 2008, arXiv.org passed the 500,000 article milestone. roughly five thousand new article added every month.[1][1] arXiv is not peer reviewed, although there are a collection of moderators for each area review the submissions and may recategorize any that are deemed off-topic.peer reviewedsubmissions High Energy Physics - Theory (since Aug 1991) High Energy Physics - Phenomenology (since Mar 1992) Astrophysics (since Apr 1992)

Is the densification a boundary (off-field) limitation of the dataset? How can we account for links that are not in the network? Example: Facebook friends that are actually friends will call each other and send off Facebook network. Will this have any effect to our view of the network density ? – not a sampling question

We are all connected

Map of Science- Different fields are connected*

What is the portion of links that are to outside-nodes? How complete is the dataset?

What are the implications of citing more and more papers & patents? Every paper can only contain a finite number of references – is a bounded problem? More references to other patents - Patents become longer with longer prosecution time and longer office actions

Percent of global Internet users who visit the site

Derek John de Solla Price studies of the exponential growth of science and the half-life of scientific literature; together with the formulation of Price's Law, namely that 25% of scientific authors are responsible for 75% of published papers (Price 1963);Price's Law quantitative studies of the network of citations between scientific papers (Price 1965), including the discovery that both the in- and out-degrees of a citation network have power-law distributions, making this the first published example of a scale-free network;scale-free network a mathematical theory of the growth of citation networks, based on what would now be called a preferential attachment process (Price 1976); [2]preferential attachment [2] an analysis of the Antikythera mechanism, an ancient Greek clockwork calculator (Price 1959, 1974).Antikythera mechanism