5 research outputs found
Comparing Community Structure to Characteristics in Online Collegiate Social Networks
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.Comment: Version 3 (17 pages, 5 multi-part figures), accepted in SIAM Revie
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High-order species interactions shape ecosystem diversity
Classical theory shows that large communities are destabilized by random interactions among species pairs, creating an upper bound on ecosystem diversity. However, species interactions often occur in high-order combinations, whereby the interaction between two species is modulated by one or more other species. Here, by simulating the dynamics of communities with random interactions, we find that the classical relationship between diversity and stability is inverted for high-order interactions. More specifically, while a community becomes more sensitive to pairwise interactions as its number of species increases, its sensitivity to three-way interactions remains unchanged, and its sensitivity to four-way interactions actually decreases. Therefore, while pairwise interactions lead to sensitivity to the addition of species, four-way interactions lead to sensitivity to species removal, and their combination creates both a lower and an upper bound on the number of species. These findings highlight the importance of high-order species interactions in determining the diversity of natural ecosystems