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This paper studies structures for efficient and stable integration of multi-community networks where establishing bridges across communities incur additional link cost compared to those within communities. Building on the connections models with direct and indirect benefits, we show that the efficient structure for homogeneous cost and benefit parameters, and for communities of arbitrary size, always has a diameter no greater than 3. We further show that for non-trivial cases, integration always follows one of these three structures: single star, two hub-connected stars, and a new structure we introduce in this paper as parallel hyperstar, which is a special core/periphery structure with parallel bridges that connect the core nodes of different communities. Then we investigate stability conditions of these structures, using the standard pairwise stability, as well as post-transfer pairwise stability, a new stability notion we introduce in this paper, which allows for bilateral utility transfers. We show that while the parallel hyperstar structure can never be both efficient and pairwise stable, once post-transfer pairwise stability is used, efficiency guarantees stability. Furthermore, we show that all possible efficient structures can be simultaneously post-transfer pairwise stable. In the end, we provide some numerical results and discussion of empirical evidences. [ABSTRACT FROM AUTHOR]

Fragmentation, echo chambers, and their amelioration in social networks have been a growing concern in the academic and non-academic world. This paper shows how, under the assumption of homophily, echo chambers and fragmentation are system-immanent phenomena of highly flexible social networks, even under ideal conditions for heterogeneity. We achieve this by finding an analytical, network-based solution to the Schelling model and by proving that weak ties do not hinder the process. Furthermore, we derive that no level of positive algorithmic bias in the form of rewiring is capable of preventing fragmentation and its effect on reducing the fragmentation speed is negligible. [ABSTRACT FROM AUTHOR]

Many social and other networks exhibit stable size scaling relationships, such that features such as mean degree or reciprocation rates change slowly or are approximately constant as the number of vertices increases. Statistical network models built on top of simple Bernoulli baseline (or reference) measures often behave unrealistically in this respect, leading to the development of sparse reference models that preserve features such as mean degree scaling. In this paper, we generalize recent work on the micro-foundations of such reference models to the case of sparse directed graphs with non-vanishing reciprocity, providing a dynamic process interpretation of the emergence of stable macroscopic behavior. [ABSTRACT FROM AUTHOR]

This paper constructs a new theory of social networks based on reputation. The model assumes that reputation is an asset and that individuals connect by buying options on the reputation of others. In networking, individuals construct portfolios of call options to leverage the reputations of others and put options to hedge the connections with others. A network then consists of portfolios of reputation options. The option model confers advantages not present in existing models. First, the payoff to connecting is the payoff on a portfolio of reputation options. Second, the network forms as individuals take option positions; the network evolves as individuals adjust those positions. Third, networking strategies become option strategies. The model allows for insights into network structure, the price of connecting and the value of connecting. [ABSTRACT FROM AUTHOR]

An important side effect of the evolution of the human brain is an increased capacity to form opinions in a very large domain of issues, which become points of aggressive interpersonal disputes. Remarkably, such disputes are often no less vigorous on small differences of opinion than large differences. Opinion differences that may be measured on the real number line may not directly correspond to the subjective importance of an issue and extent of resistance to opinion change. This is a hard problem for the field of opinion dynamics, a field that has become increasingly prominent as it has attracted more contributions to it from investigators in the natural and engineering sciences. The paper contributes a scale-free approach to assessing the extents to which individuals, with unknown heterogeneous resistances to influence, have been influenced by the opinions of others. [ABSTRACT FROM PUBLISHER]