The Routing of Complex Contagion in Kleinberg's Small-World Networks

In Kleinberg's small-world network model, strong ties are modeled as deterministic edges in the underlying base grid and weak ties are modeled as random edges connecting remote nodes. The probability of connecting a node $u$ with node $v$ through a weak tie is proportional to $1/|uv|^\alpha$, where $|uv|$ is the grid distance between $u$ and $v$ and $\alpha\ge 0$ is the parameter of the model. Complex contagion refers to the propagation mechanism in a network where each node is activated only after $k \ge 2$ neighbors of the node are activated. In this paper, we propose the concept of routing of complex contagion (or complex routing), where we can activate one node at one time step with the goal of activating the targeted node in the end. We consider decentralized routing scheme where only the weak ties from the activated nodes are revealed. We study the routing time of complex contagion and compare the result with simple routing and complex diffusion (the diffusion of complex contagion, where all nodes that could be activated are activated immediately in the same step with the goal of activating all nodes in the end). We show that for decentralized complex routing, the routing time is lower bounded by a polynomial in $n$ (the number of nodes in the network) for all range of $\alpha$ both in expectation and with high probability (in particular, $\Omega(n^{\frac{1}{\alpha+2}})$ for $\alpha \le 2$ and $\Omega(n^{\frac{\alpha}{2(\alpha+2)}})$ for $\alpha > 2$ in expectation), while the routing time of simple contagion has polylogarithmic upper bound when $\alpha = 2$. Our results indicate that complex routing is harder than complex diffusion and the routing time of complex contagion differs exponentially compared to simple contagion at sweetspot.Comment: Conference version will appear in COCOON 201

Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading

We motivate and explore the basic features of generalized contagion, a model mechanism that unifies fundamental models of biological and social contagion. Generalized contagion builds on the elementary observation that spreading and contagion of all kinds involve some form of system memory. We discuss the three main classes of systems that generalized contagion affords, resembling: simple biological contagion; critical mass contagion of social phenomena; and an intermediate, and explosive, vanishing critical mass contagion. We also present a simple explanation of the global spreading condition in the context of a small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur

Mobile Communication Signatures of Unemployment

The mapping of populations socio-economic well-being is highly constrained by the logistics of censuses and surveys. Consequently, spatially detailed changes across scales of days, weeks, or months, or even year to year, are difficult to assess; thus the speed of which policies can be designed and evaluated is limited. However, recent studies have shown the value of mobile phone data as an enabling methodology for demographic modeling and measurement. In this work, we investigate whether indicators extracted from mobile phone usage can reveal information about the socio-economical status of microregions such as districts (i.e., average spatial resolution < 2.7km). For this we examine anonymized mobile phone metadata combined with beneficiaries records from unemployment benefit program. We find that aggregated activity, social, and mobility patterns strongly correlate with unemployment. Furthermore, we construct a simple model to produce accurate reconstruction of district level unemployment from their mobile communication patterns alone. Our results suggest that reliable and cost-effective economical indicators could be built based on passively collected and anonymized mobile phone data. With similar data being collected every day by telecommunication services across the world, survey-based methods of measuring community socioeconomic status could potentially be augmented or replaced by such passive sensing methods in the future

Effects of time window size and placement on the structure of aggregated networks

Complex networks are often constructed by aggregating empirical data over time, such that a link represents the existence of interactions between the endpoint nodes and the link weight represents the intensity of such interactions within the aggregation time window. The resulting networks are then often considered static. More often than not, the aggregation time window is dictated by the availability of data, and the effects of its length on the resulting networks are rarely considered. Here, we address this question by studying the structural features of networks emerging from aggregating empirical data over different time intervals, focussing on networks derived from time-stamped, anonymized mobile telephone call records. Our results show that short aggregation intervals yield networks where strong links associated with dense clusters dominate; the seeds of such clusters or communities become already visible for intervals of around one week. The degree and weight distributions are seen to become stationary around a few days and a few weeks, respectively. An aggregation interval of around 30 days results in the stablest similar networks when consecutive windows are compared. For longer intervals, the effects of weak or random links become increasingly stronger, and the average degree of the network keeps growing even for intervals up to 180 days. The placement of the time window is also seen to affect the outcome: for short windows, different behavioural patterns play a role during weekends and weekdays, and for longer windows it is seen that networks aggregated during holiday periods are significantly different.Comment: 19 pages, 11 figure

What am I not seeing? An Interactive Approach to Social Content Discovery in Microblogs

In this paper, we focus on the informational and user experience benefits of user-driven topic exploration in microblog communities, such as Twitter, in an inspectable, controllable and personalized manner. To this end, we introduce ``HopTopics'' -- a novel interactive tool for exploring content that is popular just beyond a user's typical information horizon in a microblog, as defined by the network of individuals that they are connected to. We present results of a user study (N=122) to evaluate HopTopics with varying complexity against a typical microblog feed in both personalized and non-personalized conditions. Results show that the HopTopics system, leveraging content from both the direct and extended network of a user, succeeds in giving users a better sense of control and transparency. Moreover, participants had a poor mental model for the degree of novel content discovered when presented with non-personalized data in the Inspectable interface

Social and content hybrid image recommender system for mobile social networks

One of the advantages of social networks is the possibility to socialize and personalize the content created or shared by the users. In mobile social networks, where the devices have limited capabilities in terms of screen size and computing power, Multimedia Recommender Systems help to present the most relevant content to the users, depending on their tastes, relationships and profile. Previous recommender systems are not able to cope with the uncertainty of automated tagging and are knowledge domain dependant. In addition, the instantiation of a recommender in this domain should cope with problems arising from the collaborative filtering inherent nature (cold start, banana problem, large number of users to run, etc.). The solution presented in this paper addresses the abovementioned problems by proposing a hybrid image recommender system, which combines collaborative filtering (social techniques) with content-based techniques, leaving the user the liberty to give these processes a personal weight. It takes into account aesthetics and the formal characteristics of the images to overcome the problems of current techniques, improving the performance of existing systems to create a mobile social networks recommender with a high degree of adaptation to any kind of user

It's the Recipient That Counts: Spending Money on Strong Social Ties Leads to Greater Happiness than Spending on Weak Social Ties

Previous research has shown that spending money on others (prosocial spending) increases happiness. But, do the happiness gains depend on who the money is spent on? Sociologists have distinguished between strong ties with close friends and family and weak ties—relationships characterized by less frequent contact, lower emotional intensity, and limited intimacy. We randomly assigned participants to reflect on a time when they spent money on either a strong social tie or a weak social tie. Participants reported higher levels of positive affect after recalling a time they spent on a strong tie versus a weak tie. The level of intimacy in the relationship was more important than the type of relationship; there was no significant difference in positive affect after recalling spending money on a family member instead of a friend. These results add to the growing literature examining the factors that moderate the link between prosocial behaviour and happiness