The Small-Community Phenomenon in Networks

We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost) every one in our society belongs to some meaningful small communities by the authors (2011), and that under certain conditions on the parameters, the power law degree distribution, which significantly strengths the results given by van den Esker (2008), and Jordan (2010). The results above, together with our previous progress in Li and Peng (2011), build a mathematical foundation for the study of communities and the small-community phenomenon in various networks. In the proof of the power law degree distribution, we develop the method of alternating concentration analysis to build concentration inequality by alternatively and iteratively applying both the sub- and super-martingale inequalities, which seems powerful, and which may have more potential applications.Comment: 23 page

Local interactions and the emergence of a Twitter small-world network

The small-world phenomenon is found in many self-organising systems. Systems configured in small-world networks spread information more easily than in random or regular lattice-type networks. Whilst it is a known fact that small-world networks have short average path length and high clustering coefficient in self-organising systems, the ego centralities that maintain the cohesiveness of small-world network have not been formally defined. Here we show that instantaneous events such as the release of news items via Twitter, coupled with active community arguments related to the news item form a particular type of small-world network. Analysis of the centralities in the network reveals that community arguments maintain the small-world network whilst actively maintaining the cohesiveness and boundary of the group. The results demonstrate how an active Twitter community unconsciously forms a small-world network whilst interacting locally with a bordering community. Over time, such local interactions brought about the global emergence of the small-world network, connecting media channels with human activities. Understanding the small-world phenomenon in relation to online social or civic movement is important, as evident in the spate of online activists that tipped the power of governments for the better or worst in recent times. The support, or removal of high centrality nodes in such networks has important ramifications in the self-expression of society and civic discourses. The presentation in this article anticipates further exploration of man-made self-organising systems where a larger cluster of ad-hoc and active community maintains the overall cohesiveness of the network

Super-resolution community detection for layer-aggregated multilayer networks

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the tradeoffs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with $N$ nodes and $L$ layers, which are drawn from an ensemble of Erd\H{o}s-R\'enyi networks. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit $K^*$. When layers are aggregated via a summation, we obtain $K^*\varpropto \mathcal{O}(\sqrt{NL}/T)$, where $T$ is the number of layers across which the community persists. Interestingly, if $T$ is allowed to vary with $L$ then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that $T/L$ decays more slowly than $\mathcal{O}(L^{-1/2})$. Moreover, we find that thresholding the summation can in some cases cause $K^*$ to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. That is, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.Comment: 11 pages, 8 figure

Chinese entrepreneurs and workers at the crossroad: the role of social networks in ethnic industrial clusters in Italy

PurposeThis paper aims to analyse the evolution of Chinese industrial ethnic clusters in Italy, by focusing on the role of social networks and the processes behind the phenomenon of Chinese worker exploitation and entrepreneur "self-exploitation".Design/methodology/approachThe case study is a sub-cluster of micro and small enterprises owned by Chinese entrepreneurs within the leather industrial district of Florence, Italy. This research adopts the following mixed methods: a small-scale survey to capture the characteristics of the sub-cluster and a social network analysis to describe cluster evolution, complemented by life-course interviews conducted with key informants and entrepreneurs.FindingsMigrant social capital and social networks play a central role in the evolution of the case study sub-cluster. Social networks play a supportive role in migration, job creation, entrepreneurship formation and the creation of business opportunities. Simultaneously, they enhance the phenomenon of worker exploitation and entrepreneur self-exploitation. Furthermore, the more the business community grows, the more the economic performance of ethnic enterprises depends on agglomeration forces produced by the cluster.Practical implicationsThe findings suggest a series of potential policies to upgrade the ethnic enterprises' capacities, to increase their formality and inclusion in the Italian social and economic systems and sub-cluster.Originality/valueTo the authors' knowledge, this paper is the first attempt to examine the evolution of social networks in relation to the phenomenon of Chinese worker exploitation and entrepreneur self-exploitation in an ethnic industrial sub-cluster