Link-Prediction to Tackle the Boundary Specification Problem in Social Network Surveys

Diffusion processes in social networks often cause the emergence of global phenomena from individual behavior within a society. The study of those global phenomena and the simulation of those diffusion processes frequently require a good model of the global network. However, survey data and data from online sources are often restricted to single social groups or features, such as age groups, single schools, companies, or interest groups. Hence, a modeling approach is required that extrapolates the locally restricted data to a global network model. We tackle this Missing Data Problem using Link-Prediction techniques from social network research, network generation techniques from the area of Social Simulation, as well as a combination of both. We found that techniques employing less information may be more adequate to solve this problem, especially when data granularity is an issue. We validated the network models created with our techniques on a number of real-world networks, investigating degree distributions as well as the likelihood of links given the geographical distance between two nodes

Group definition.

<p>Group definition.</p

Network created by combined approach.

<p>The Figure presents the individual pupils that participated in the FUNDAJ-Survey. Pupils are colored according to their school. Location of pupils is assigned by a Fruchtermann-Reingold algorithm within a radius of <i>n</i>² around the location of their school within the city of Recife. <i>n</i> indicates the number of pupils of the respective school. Grey lines indicate friendships between pupils as registered by the survey, as well as friendships estimated by the combined method applying <i>c</i> = 300.</p

Reference values.

<p>Reference values.</p

Log-Log plot of survival function (CCDF).

<p>Link-probability related to physical distance between nodes for networks generated with Social Circles (c = 500), Bootstrapping(r = 0.91) and Combined approach (c = 800). Compared to distance- link-probability distributions from real world social networks: Brightkite and Gowalla worldwide networks, as well as local sub networks for the city of New York.</p

Combined approach objective values.

<p>The abscissa scales the different values of the parameter <i>c</i> that controls the exponent of the exponential decay function in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176094#pone.0176094.e007" target="_blank">Eq 7</a>; objective ranges and upper-/lower limits are indicated by dashed lines.</p

School-clusters from Recife.

<p>The Figure presents the individual pupils that participated in the FUNDAJ-Survey. Pupils are colored according to their school. Location of pupils is assigned by a Fruchtermann-Reingold algorithm [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176094#pone.0176094.ref036" target="_blank">36</a>] centered around the location of their school within the city of Recife. Grey lines indicate friendships between pupils as registered by the survey. As social networks where solely surveyed within schools, isolated components appear for each school.</p

Social circles—Objective values.

<p>The abscissa scales the different values of the parameter <i>c</i> that controls the exponent of the exponential decay function in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0176094#pone.0176094.e001" target="_blank">Eq 1</a>; objective ranges and upper-/lower limits are indicated by dashed lines.</p

Bootstrapping objective values.

<p>The abscissa scales the different values of the threshold parameter <i>r</i>; objective ranges and upper-/lower limits are indicated by dashed lines.</p

Network created by bootstrapping.

<p>The Figure presents the individual pupils that participated in the FUNDAJ-Survey. Pupils are colored according to their school. Location of pupils is assigned by a Fruchtermann-Reingold algorithm within a radius of <i>n</i>² around the location of their school within the city of Recife. <i>n</i> indicates the number of pupils of the respective school. Grey lines indicate friendships between pupils as registered by the survey, as well as friendships estimated by the Bootstrapping method applying <i>r</i> = 0.91.</p