Balance theory has advanced with interdisciplinary contributions from social science, physical science, engineering, and mathematics. The common focus of attention is social networks in which every individual has either a positive or negative, cognitive or emotional, appraisal of every other individual. The current frontier of work on balance theory is a hunt for a dynamical model that predicts the temporal evolution of any such appraisal network to a particular structure in the complete set of balanced networks allowed by the theory. Finding such a model has proved to be a difficult problem. In this article, we contribute a parsimonious solution of the problem that explicates the conditions under which a network will evolve either to a set of mutually antagonistic cliques or to an asymmetric structure that allows agreement, cooperation, and compromise among cliques.

We investigate the implications of different forms of multigroup connectivity. Four multigroup connectivity modalities are considered: co-memberships, edge bundles, bridges, and liaison hierarchies. We propose generative models to generate these four modalities. Our models are variants of planted partition or stochastic block models conditioned under certain topological constraints. We report findings of a comparative analysis in which we evaluate these structures, controlling for their edge densities and sizes, on mean rates of information propagation, convergence times to consensus, and steady-state deviations from the consensus value in the presence of noise as network size increases.

Network science gathers methods coming from various disciplines which sometimes hardly cross the boundaries between these disciplines. Widely used in molecular biology in the study of protein interaction networks, the enumeration, in a network, of all possible subgraphs of a limited size (usually around four or five nodes), often called graphlets, can only be found in a few works dealing with social networks. In the present work, we apply this approach to an original corpus of about 10,000 non-overlapping Facebook ego networks gathered from voluntary participants by a survey application. To deal with so many similar networks, we adapt the relative graphlet frequency to a measure that we call graphlet representativity, which we show to be more effective to classify random networks having slight structural differences. From our data, we produce two clusterings, one of graphlets (paths, star-like, holes, light triangles, and dense), one of networks. The latter is presented with a visualization scheme using our representativity measure. We describe the distinct structural characteristics of the five clusters of Facebook ego networks so obtained and discuss the empirical differences between results obtained with 4-node and 5-node graphlets. We also provide suggestions of follow-ups of this work, both in sociology and in network science.

Values—the motivational goals that define what is important to us—guide our decisions and actions every day. Their importance is established in a long line of research investigating their universality across countries and their evolution from childhood to adulthood. In adolescence, value structures are subject to substantial change, as life becomes increasingly social. Value change has thus far been understood to operate independently within each person. However, being embedded in various social systems, adolescents are constantly subject to social influence from peers. Thus, we introduce a framework investigating the emergence and evolution of value priorities in the dynamic context of friendship networks. Drawing on stochastic actor-oriented network models, we analyze 73 friendship networks of adolescents. Regarding the evolution of values, we find that adolescents’ value systems evolve in a continuous cycle of internal validation through the selection and enactment of goals—thereby experiencing both congruence and conflicts—and external validation through social comparison among their friends. Regarding the evolution of friendship networks, we find that demographics are more salient for the initiation of new friendships, whereas values are more relevant for the maintenance of existing friendships.

Though declining since the 1990s, adolescent pregnancy remains common in the United States. Social supports appear to improve outcomes for pregnant teens; however, teen pregnancy introduces social obstacles, such as stigma. This study investigates how currently or previously pregnant teens’ friendship networks differ from nonpregnant girls using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health) and multilevel regression models. To mitigate concerns that background differences contribute to both pregnancy risk and social networks, girls who experience a pregnancy prior to one data collection time point are compared girls who experience their first pregnancy after this time point. This group who become pregnant after the time point is presumably more similar to already pregnant teens than those never experiencing teen pregnancy. When compared to these girls who become pregnant in the future, those who have already experienced a teen pregnancy report similar numbers of friends (out-nominations) and perceived social acceptance, but are predicted to have fewer peers reporting them as friends (in-nominations) and fewer reciprocated friendships. This suggests that pregnant teens may face stigmatization, of which they may be unaware. It further highlights a new comparison group to account for selection in studies of adolescent pregnancy.

One of the most challenging problems in biomedicine and genomics is the identification of disease biomarkers. In this study, proteomics data from seven major cancers were used to construct two weighted protein–protein interaction networks, i.e., one for the normal and another for the cancer conditions. We developed rigorous, yet mathematically simple, methodology based on the degeneracy at –1 eigenvalues to identify structural symmetry or motif structures in network. Utilizing eigenvectors corresponding to degenerate eigenvalues in the weighted adjacency matrix, we identified structural symmetry in underlying weighted protein–protein interaction networks constructed using seven cancer data. Functional assessment of proteins forming these structural symmetry exhibited the property of cancer hallmarks. Survival analysis refined further this protein list proposing BMI, MAPK11, DDIT4, CDKN2A, and FYN as putative multicancer biomarkers. The combined framework of networks and spectral graph theory developed here can be applied to identify symmetrical patterns in other disease networks to predict proteins as potential disease biomarkers.

We introduce a weighted configuration model graph, where edge weights correspond to the probability of infection in an epidemic on the graph. On these graphs, we study the development of a Susceptible–Infectious–Recovered epidemic using both Reed–Frost and Markovian settings. For the special case of having two different edge types, we determine the basic reproduction numberR0, the probability of a major outbreak, and the relative final size of a major outbreak. Results are compared with those for a calibrated unweighted graph. The degree distributions are based on both theoretical constructs and empirical network data. In addition, bivariate standard normal copulas are used to model the dependence between the degrees of the two edge types, allowing for modeling the correlation between edge types over a wide range. Among the results are that the weighted graph produces much richer results than the unweighted graph. Also, while R0 always increases with increasing correlation between the two degrees, this is not necessarily true for the probability of a major outbreak nor for the relative final size of a major outbreak. When using copulas we see that these can produce results that are similar to those of the empirical degree distributions, indicating that in some cases a copula is a viable alternative to using the full empirical data.