A preference for diversity has been identified as an important predictor of tie formation in certain networks, both social and organizational, that also exhibit a high degree of suppleness–the ability to retain their general form and character under stress (Durkheim, 1893/1997. The division of labor in society; Powell et al., 1996. Administrative Science Quarterly 116–145; Powell et al., 2005. American Journal of Sociology, 110(4), 1132–1205; Koput & Gutek, 2010. Gender stratification in the IT industry: Sex, status and social capital. Edward Elgar Publishing). Extant models of preferential attachment, based on popularity, similarity, and cohesion, meanwhile, produce exceedingly brittle networks (Albert et al., 2000. Nature, 406(6794), 378–382; Callaway et al., 2000. Physical Review Letters, 85(25), 5468–5471; Holme et al., 2002. Physical Review E, 65(2), 026107; Shore et al., 2013 Social Networks, 35(1), 116–123). A model of preferential attachment based on diversity is introduced and simulated, demonstrating that a preference for diversity can create a structure characterized by suppleness. This occurs because a preference for diversity promotes overlapping and redundant weak ties during the early stages of network formation.

As social networks evolve, new nodes are linked to the large-scale organization already in place. We show that the combination of two simple algorithms, one the Barabasi-Albert preferential attachment proposal and the other a neighbor attachment rule, successfully generate networks exhibiting both the local and global characteristics of empirical data on social network structures. Ideally, one might hope that some coarse features of this linking process and the form of the local patterns might enable the prediction of large-scale properties. We show that this is generally not the case. This might help explain the variety of local and global patterns in empirical networks.

Peer-to-peer systems have driven a lot of attention in the past decade as they have become a major source of Internet traffic. The amount of data flowing through the peer-to-peer network is huge and hence challenging both to comprehend and to control. In this work, we take advantage of a new and rich dataset recording the peer-to-peer activity at a remarkable scale to address these difficult problems. After extracting the relevant and measurable properties of the network from the data, we develop two models that aim to make the link between the low-level properties of the network, such as the proportion of peers that do not share content (i.e., free riders) or the distribution of the files among the peers, and its high-level properties, such as the Quality of Service or the diffusion of content, which are of interest for supervision and control purposes. We observe a significant agreement between the high-level properties measured on the real data and on the synthetic data generated by our models, which is encouraging for our models to be used in practice as large-scale prediction tools. Relying on them, we demonstrate that spending efforts to reduce the amount of free riders indeed helps to improve the availability of files on the network. We observe however a saturation of this phenomenon after 60% of free riders.

We study the network structure of Wikipedia (restricted to its mathematical portion), MathWorld, and DLMF. We approach these three online mathematical libraries from the perspective of several global and local network-theoretic features, providing for each one the appropriate value or distribution, along with comparisons that, if possible, also include the whole of the Wikipedia or the Web. We identify some distinguishing characteristics of all three libraries, most of them supposedly traceable to the libraries' shared nature of relating to a very specialized domain. Among these characteristics are the presence of a very large strongly connected component in each of the corresponding directed graphs, the complete absence of any clear power laws describing the distribution of local features, and the rise to prominence of some local features (e.g., stress centrality) that can be used to effectively search for keywords in the libraries.

Real world networks typically have large clustering coefficients. The clustering coefficient can be interpreted to be the result of a triangle closing mechanism. We have here enumerated cliques and maximal cliques in multiple networks to show that real world networks have a high number of large cliques. While triangles are more frequent than expected, large cliques are much more over-expressed, and the largest difference between real world networks and their random counterpart occurs in many networks at clique sizes of 5–7, and not at a size of 3. This does not result from the existence of few very large cliques, since a similar feature is observed when studying only maximal cliques (cliques that are not contained in other larger cliques). Moreover, when the large cliques are removed, triangles are often under-expressed.

In all networks studied but one, all node members of large cliques produce a single connected component, which represent the central “core” of the network. The observed clique distribution can be explained by multiple models, mainly hidden variables model, such as the gravitation model, or the collapse of bipartite networks. These models can explain other properties of these networks, including the sub-graph distribution and the distance distribution of the networks. This suggests that node connectivity in real world networks may be determined by the similarity between the contents of the networks' nodes. This is in contrast with models of network formation that incorporate only the properties of the network, and not the internal properties of the nodes.

Real-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(VS, VT, ES, ET, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.

An incredible number of centrality indices has been proposed to date (Todeschini & Consonni, 2009). Four of them, however, can be considered prototypical because they operationalize distinct concepts of centrality and together cover the bulk of analyses and empirical uses: degree, closeness, betweenness, and eigenvector centrality.