Comparing Community Structure to Characteristics in Online Collegiate Social Networks

Abstract

Abstract. We study the structure of social networks of students by examining the graphs of Facebook "friendships" at five American universities at a single point in time. We investigate each single-institution network's community structure and employ graphical and quantitative tools, including standardized pair-counting methods, to measure the correlations between the network communities and a set of self-identified user characteristics (residence, class year, major, and high school). We review the basic properties and statistics of the pair-counting indices employed and recall, in simplified notation, a useful analytical formula for the z-score of the Rand coefficient. Our study illustrates how to examine different instances of social networks constructed in similar environments, emphasizes the array of social forces that combine to form "communities," and leads to comparative observations about online social lives that can be used to infer comparisons about offline social structures. In our illustration of this methodology, we calculate the relative contributions of different characteristics to the community structure of individual universities and subsequently compare these relative contributions at different universities, measuring for example the importance of common high school affiliation to large state universities and the varying degrees of influence common major can have on the social structure at different universities. The heterogeneity of communities that we observe indicates that these networks typically have multiple organizing factors rather than a single dominant one.

Extraction of force-chain network architecture in granular materials using community detection

“…To determine whether the estimates are robust to this amount of noise, we compare the community structure of the actual force networks with those of the simulated force networks using the z-score of the Rand coefficient [62]. For comparing two partitions α and β, we calculate the Rand z-score in terms of the network's total number M of pairs of nodes, the number M α of pairs that are in the same community in partition α, the number M β of pairs that are in the same community in partition β, and the number w αβ of pairs that are assigned to the same community both in partition α and in partition β.…”

“…where σ w αβ is the standard deviation of w αβ (as in [62]). Let the mean partition similarity z denote the mean value of z αβ over all possible partition pairs for α = β.…”

Untangling Hairballs

“…As real world samples, we use the Facebook100 dataset [26], which contains social relations of 100 higher educational institutes in the US. The network size varies from 762 to 41K vertices and from 16K to 1.6M edges.…”

“…Due to incomplete profiles, a number of attribute values are missing. We will use the dormitory attribute for our evaluation, because it has been argued to be important for the creation of social relations in many of the networks [26]. Note that, in spite of a strong empirical association with homophilous attribute values, no ground-truth group structure is available for Facebook networks.…”

An Introduction to Community Detection in Multi-layered Social Network

“…Depending on the type of social network we want to build, data can be found in various places, e.g. : blogs [1], telecommunication data [2], bibliographic data [3], social services like Facebook [9], e-mail systems [10] and more. Group extraction is among those topics which arouse the greatest interest in the domain of social network analysis.…”