We study how people select their health support ties from their broader personal networks, taking into account the interplay of web-based and face-to-face interactions. We focus on users of self-styled Internet communities on eating disorders, often dubbed “pro-ana” and “pro-mia” and widely feared to contribute to maintaining and spreading these disorders. Despite the controversial anti-medical stances of some of them, “ana-mia” websites may channel mutual assistance, advice, and psychological and emotional support, with ultimate benefits for health.

In 2011–12 we fielded an online survey of users of French- and English-language “ana-mia” websites, mapping the composition and structure of their personal networks both online and face-to-face, and their health and eating-related support networks, for two types of health issues. We estimate binary choice models for these data and find that different health needs call for different types of support, embedded in different parts of personal networks. Specifically, online groups provide distinctive sources of help, which partly compensate for perceived shortcomings in healthcare services, although members do not overwhelmingly reject standard health systems and norms. We discuss how web-based groups constitute an important source of social support, and a potential resource for enhanced public health services provision.

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.

A fundamental goal of systems biology is to create models that describe relationships between biological components. Networks are an increasingly popular approach to this problem. However, a scientist interested in modeling biological (e.g., gene expression) data as a network is quickly confounded by the fundamental problem: how to construct the network? It is fairly easy to construct a network, but is it the network for the problem being considered? This is an important problem with three fundamental issues: How to weight edges in the network in order to capture actual biological interactions? What is the effect of the type of biological experiment used to collect the data from which the network is constructed? How to prune the weighted edges (or what cut-off to apply)? Differences in the construction of networks could lead to different biological interpretations.

Indeed, we find that there are statistically significant dissimilarities in the functional content and topology between gene co-expression networks constructed using different edge weighting methods, data types, and edge cut-offs. We show that different types of known interactions, such as those found through Affinity Capture-Luminescence or Synthetic Lethality experiments, appear in significantly varying amounts in networks constructed in different ways. Hence, we demonstrate that different biological questions may be answered by the different networks. Consequently, we posit that the approach taken to build a network can be matched to biological questions to get targeted answers. More study is required to understand the implications of different network inference approaches and to draw reliable conclusions from networks used in the field of systems biology.

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.

Mobile phones are spreading to remote areas of the globe, leading to the following question: “What is the potential of the new communication technologies for increasing individuals' access to information and the diffusion of attitudes and practices across rural areas of developing countries?” We have donated phones to 234 farmers selected by stratified random sampling in an agrarian region of Ethiopia and have tracked their main communication partners for six months. The panel data and qualitative interviews indicated that the phones were not typically used to expand the existing constrained social networks or to gain information from new sources but to call contacts who had been known personally and to individuals introduced through the experiment. Stochastic actor-based network models clarified that although agricultural information-seeking and casual calling are intertwined, the mechanisms underlying the evolution of instrumental and expressive communication networks are distinct. Acquaintances living beyond comfortable walking distances and individuals whom others call became preferred for information-seeking calls. Thus, mobile phones may accelerate information exchange within existing social networks and may support the creation of new information hubs that might facilitate more efficient information diffusion over long distances in the future. In contrast, the importance of geographical communities strongly prevails in casual phone conversations. Physically proximate community members who tend to be met frequently were preferred for sentiment-sharing calls. Preferential attachment was not evident for this type of communication. As a result, the network of these expressive calls was highly localized and fragmented, making it unlikely for personal feelings to diffuse across wide geographical areas through the new phone networks.

Time plays an essential role in the diffusion of information, influence, and disease over networks. In many cases we can only observe when a node is activated by a contagion—when a node learns about a piece of information, makes a decision, adopts a new behavior, or becomes infected with a disease. However, the underlying network connectivity and transmission rates between nodes are unknown. Inferring the underlying diffusion dynamics is important because it leads to new insights and enables forecasting, as well as influencing or containing information propagation. In this paper we model diffusion as a continuous temporal process occurring at different rates over a latent, unobserved network that may change over time. Given information diffusion data, we infer the edges and dynamics of the underlying network. Our model naturally imposes sparse solutions and requires no parameter tuning. We develop an efficient inference algorithm that uses stochastic convex optimization to compute online estimates of the edges and transmission rates. We evaluate our method by tracking information diffusion among 3.3 million mainstream media sites and blogs, and experiment with more than 179 million different instances of information spreading over the network in a one-year period. We apply our network inference algorithm to the top 5,000 media sites and blogs and report several interesting observations. First, information pathways for general recurrent topics are more stable across time than for on-going news events. Second, clusters of news media sites and blogs often emerge and vanish in a matter of days for on-going news events. Finally, major events, for example, large scale civil unrest as in the Libyan civil war or Syrian uprising, increase the number of information pathways among blogs, and also increase the network centrality of blogs and social media sites.

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.

The analysis of complex networks has so far revolved mainly around the role of nodes and communities of nodes. However, the dynamics of interconnected systems is often focalized on edge processes, and a dual edge-centric perspective can often prove more natural. Here we present graph-theoretical measures to quantify edge-to-edge relations inspired by the notion of flow redistribution induced by edge failures. Our measures, which are related to the pseudo-inverse of the Laplacian of the network, are global and reveal the dynamical interplay between the edges of a network, including potentially non-local interactions. Our framework also allows us to define the embeddedness of an edge, a measure of how strongly an edge features in the weighted cuts of the network. We showcase the general applicability of our edge-centric framework through analyses of the Iberian power grid, traffic flow in road networks, and the C. elegans neuronal network.

Homophily—the tendency for individuals to associate with similar others—is one of the most persistent findings in social network analysis. Its importance is established along the lines of a multitude of sociologically relevant dimensions, e.g. sex, ethnicity and social class. Existing research, however, mostly focuses on one dimension at a time. But people are inherently multidimensional, have many attributes and are members of multiple groups. In this article, we explore such multidimensionality further in the context of network dynamics. Are friendship ties increasingly likely to emerge and persist when individuals have an increasing number of attributes in common? We analyze eleven friendship networks of adolescents, draw on stochastic actor-oriented network models and focus on the interaction of established homophily effects. Our results indicate that main effects for homophily on various dimensions are positive. At the same time, the interaction of these homophily effects is negative. There seems to be a diminishing effect for having more than one attribute in common. We conclude that studies of homophily and friendship formation need to address such multidimensionality further.

There is a growing consensus that dark networks require special methodological considerations, but little attention has been devoted to determining which data transformation processes are best suited to the study of dark networks. Standard approaches to the transformation of multi-modal data “fold” matrices, by binarizing the network and multiplying it against its transpose. Unfortunately, this process produces exaggerated results when applied to weighted networks, and consequently researchers often disregard information on tie-strength when transforming data. This paper evaluates previous attempts to overcome this limitation and assesses projection methods discovered by biologists and physicists, who have studied the problem of transforming weighted multi-modal networks within the specific context of these disciplines. However, the assumptions underlying these transformation processes limit their applicability to dark networks. This paper, therefore, offers the Median Additive Projection Process (MAPP), an approach to data transformation specifically designed for implementation in weighted, multi-modal dark networks. MAPP accounts for the ambiguity inherent to clandestine subject matter by treating relationship strength in a probabilistic fashion. Because agents' one-mode centrality rankings change significantly when different projection processes are applied to the same two-mode network, MAPP allows researchers to more accurately identify central actors in dark networks.

There is empirical evidence suggesting that a person's family, friends, or social ties influence who a person votes for. Sokhey & McClurg (2012) find that as political disagreement in a person's social network increases, then a person is less likely to vote correctly. We develop a model where voters have different favorite policies and wish to vote correctly for the candidate whose favorite policy is closest to their own. Voters have beliefs about each candidate's favorite policy which may or may not be correct. Voters update their beliefs about political candidates based on who their conservative and liberal social ties are supporting. We find that if everyone's social network consists only of those most like themselves, then the conditions needed for correct voting to be stable are fairly weak; thus political agreement in one's social network facilitates correct voting. We also give conditions under which correct voting is stable for networks exhibiting homophily and for networks exhibiting random social interactions.

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.

Graph kernels for learning and inference on sparse graphs have been widely studied. However, the problem of designing robust kernel functions that can effectively compare graph neighborhoods in the presence of noisy and complex data remains less explored. Here we propose a novel graph-based kernel method referred to as an edit distance graphlet kernel. The method was designed to add flexibility in capturing similarities between local graph neighborhoods as a means of probabilistically annotating vertices in sparse and labeled graphs. We report experiments on nine real-life data sets from molecular biology and social sciences and provide evidence that the new kernels perform favorably compared to established approaches. However, when both performance accuracy and run time are considered, we suggest that edit distance kernels are best suited for inference on graphs derived from protein structures. Finally, we demonstrate that the new approach facilitates simple and principled ways of integrating domain knowledge into classification and point out that our methodology extends beyond classification; e.g. to applications such as kernel-based clustering of graphs or approximate motif finding. Availability: www.sourceforge.net/projects/graphletkernels/

Recent research indicates that knowledge about social networks can be leveraged to increase efficiency of interventions (Valente, 2012). However, in many settings, there exists considerable uncertainty regarding the structure of the network. This can render the estimation of potential effects of network-based interventions difficult, as providing appropriate guidance to select interventions often requires a representation of the whole network. In order to make use of the network property estimates to simulate the effect of interventions, it may be beneficial to sample networks from an estimated posterior predictive distribution, which can be specified using a wide range of models. Sampling networks from a posterior predictive distribution of network properties ensures that the uncertainty about network property parameters is adequately captured. The tendency for relationships among network properties to exhibit sharp thresholds has important implications for understanding global network topology in the presence of uncertainty; therefore, it is essential to account for uncertainty. We provide detail needed to sample networks for the specific network properties of degree distribution, mixing frequency, and clustering. Our methods to generate networks are demonstrated using simulated data and data from the National Longitudinal Study of Adolescent Health.

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.

In this paper we examine natural generalizations of four widely used centrality measures to subgroups of nodes in a network. This allows for a division into local and global influence. As an example, we analyze a classic network and discuss previously hidden features made visible by these new techniques. Network-wide measures and centralization formulae are derived.

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.

The spreading of transmissible infectious diseases is inevitably entangled with the dynamics of human population. Humans are the carrier of the pathogen, and the large-scale travel and commuting patterns that govern the mobility of modern societies are defining how epidemics and pandemics travel across the world. For a long time, the development of quantitative spatially explicit models able to shed light on the global dynamics of pandemic has been limited by the lack of detailed data on human mobility. In the last 10 years, however, these limits have been lifted by the increasing availability of data generated by new information technologies, thus triggering the development of computational (microsimulation) models working at a level of single individuals in spatially extended regions of the world. Microsimulations can provide information at very detailed spatial resolutions and down to the level of single individuals. In addition, computational implementations explicitly account for stochasticity, allowing the study of multiple realizations of epidemics with the same parameters' distribution. While on the one hand these capabilities represent the richness of microsimulation methods, on the other hand they face us with a huge amount of information that requires the use of specific data reduction methods and visual analytics.

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.