The definition of suitable generative models for synthetic yet realistic social networks is a widely studied problem in the literature. By not being tied to any real data, random graph models cannot capture all the subtleties of real networks and are inadequate for many practical contexts—including areas of research, such as computational epidemiology, which are recently high on the agenda. At the same time, the so-called contact networks describe interactions, rather than relationships, and are strongly dependent on the application and on the size and quality of the sample data used to infer them. To fill the gap between these two approaches, we present a data-driven model for urban social networks, implemented and released as open source software. By using just widely available aggregated demographic and social-mixing data, we are able to create, for a territory of interest, an age-stratified and geo-referenced synthetic population whose individuals are connected by “strong ties” of two types: intra-household (e.g., kinship) or friendship. While household links are entirely data-driven, we propose a parametric probabilistic model for friendship, based on the assumption that distances and age differences play a role, and that not all individuals are equally sociable. The demographic and geographic factors governing the structure of the obtained network, under different configurations, are thoroughly studied through extensive simulations focused on three Italian cities of different size.

Tor is an open source software that allows accessing various kinds of resources, known as hidden services, while guaranteeing sender and receiver anonymity. Tor relies on a free, worldwide, overlay network, managed by volunteers, that works according to the principles of onion routing in which messages are encapsulated in layers of encryption, analogous to layers of an onion. The Tor Web is the set of web resources that exist on the Tor network, and Tor websites are part of the so-called dark web. Recent research works have evaluated Tor security, its evolution over time, and its thematic organization. Nevertheless, limited information is available about the structure of the graph defined by the network of Tor websites, not to be mistaken with the network of nodes that supports the onion routing. The limited number of entry points that can be used to crawl the network, makes the study of this graph far from being simple. In the present paper we analyze two graph representations of the Tor Web and the relationship between contents and structural features, considering three crawling datasets collected over a five-month time frame. Among other findings, we show that Tor consists of a tiny strongly connected component, in which link directories play a central role, and of a multitude of services that can (only) be reached from there. From this viewpoint, the graph appears inefficient. Nevertheless, if we only consider mutual connections, a more efficient subgraph emerges, that is, probably, the backbone of social interactions in Tor.

Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose properties may be tuned upon the characteristics of a given population. In the present paper, we introduce the Fitness-Corrected Block Model, an adjustable-density variation of the well-known Degree-Corrected Block Model, and we show that the proposed construction yields a maximum entropy model. When the network is sparse, we derive an analytical expression for the degree distribution of the model that depends on just the constraints and the chosen fitness-distribution. Our model is perfectly suited to define maximum-entropy data-driven spatial social networks, where each block identifies vertices having similar position (e.g., residence) and age, and where the expected block-to-block adjacency matrix can be inferred from the available data. In this case, the sparse-regime approximation coincides with a phenomenological model where the probability of a link binding two individuals is directly proportional to their sociability and to the typical cohesion of their age-groups, whereas it decays as an inverse-power of their geographic distance. We support our analytical findings through simulations of a stylized urban area.