Characteristics of Small Social Networks

Two dozen networks are analyzed using three parameters that attempt to capture important properties of social networks: leadership L, member bonding B, and diversity of expertise D. The first two of these parameters have antecedents, the third is new. A key part of the analysis is to examine networks at multiple scales by dissecting the entire network into its n subgraphs of a given radius of two edge steps about each of the n nodes. This scale-based analysis reveals constraints on what we have dubbed "cognitive" networks, as contrasted with biological or physical networks. Specifically, "cognitive" networks appear to maximize bonding and diversity over a range of leadership dominance. Asymptotic relations between the bonding and diversity measures are also found when small, nearly complete subgraphs are aggregated to form larger networks. This aggregation probably underlies changes in a regularity among the LBD parameters; this regularity is a U-shaped function of networks size, n, which is minimal for networks around 80 or so nodes

Investigating the fine grained structure of networks

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 107-109).In this thesis I explore a novel representation for characterizing a graph's fine grained structure. The key idea is that this structure can be represented as a distribution of the structural features of subgraphs. I introduce a set of such structural features and use them to compute representations for a variety of graphs, demonstrating their use in qualitatively describing fine structure. I then demonstrate the utility of this representation with quantitative techniques for computing graph similarity and graph clustering. I show that similarity judged using this representation is significantly different from judgements using full graph structural measures. I find that graphs from the same class of networks, such as email correspondence graphs, can differ significantly in their fine structure across the institutions whose relations they model, but also find examples of graphs from the same institutions across different time periods that share a similar fine structure.by Owen Macindoe.S.M