Trends Prediction Using Social Diffusion Models

The importance of the ability of predict trends in social media has been growing rapidly in the past few years with the growing dominance of social media in our everyday's life. Whereas many works focus on the detection of anomalies in networks, there exist little theoretical work on the prediction of the likelihood of anomalous network pattern to globally spread and become "trends". In this work we present an analytic model the social diffusion dynamics of spreading network patterns. Our proposed method is based on information diffusion models, and is capable of predicting future trends based on the analysis of past social interactions between the community's members. We present an analytic lower bound for the probability that emerging trends would successful spread through the network. We demonstrate our model using two comprehensive social datasets - the "Friends and Family" experiment that was held in MIT for over a year, where the complete activity of 140 users was analyzed, and a financial dataset containing the complete activities of over 1.5 million members of the "eToro" social trading community.Comment: 6 Pages + Appendi

Experimental evidence for tipping points in social convention

Theoretical models of critical mass have shown how minority groups can initiate social change dynamics in the emergence of new social conventions. Here we study an artificial system of social conventions in which human subjects interact to establish a new coordination equilibrium. The findings provide direct empirical demonstration of the existence of a tipping point in the dynamics of changing social conventions. When minority groups reached the critical mass –that is, the critical group size for initiating social change –they were consistently able to overturn the established behavior. The size of the required critical mass is expected to vary based on theoretically identifiable features of a social setting. Our results show that the theoretically predicted dynamics of critical mass do in fact emerge as expected within an empirical system of social coordination

Trends Prediction Using Social Diffusion Models

The importance of the ability to predict trends in social media has been growing rapidly in the past few years with the growing dominance of social media in our everyday’s life. Whereas many works focus on the detection of anomalies in networks, there exist little theoretical work on the prediction of the likelihood of anomalous network pattern to globally spread and become “trends”. In this work we present an analytic model for the social diffusion dynamics of spreading network patterns. Our proposed method is based on information diffusion models, and is capable of predicting future trends based on the analysis of past social interactions between the community’s members. We present an analytic lower bound for the probability that emerging trends would successfully spread through the network. We demonstrate our model using two comprehensive social datasets — the Friends and Family experiment that was held in MIT for over a year, where the complete activity of 140 users was analyzed, and a financial dataset containing the complete activities of over 1.5 million members of the eToro social trading community

Generic Absorbing Transition in Coevolution Dynamics

We study a coevolution voter model on a network that evolves according to the state of the nodes. In a single update, a link between opposite-state nodes is rewired with probability $p$, while with probability $1-p$ one of the nodes takes its neighbor's state. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value $p_c=\frac{\mu-2}{\mu-1}$ that only depends on the average degree $\mu$ of the network. The approach to the final state is characterized by a time scale that diverges at the critical point as $\tau \sim |p_c-p|^{-1}$. We find that the active and frozen phases correspond to a connected and a fragmented network respectively. We show that the transition in finite-size systems can be seen as the sudden change in the trajectory of an equivalent random walk at the critical rewiring rate $p_c$, highlighting the fact that the mechanism behind the transition is a competition between the rates at which the network and the state of the nodes evolve.Comment: 5 pages, 4 figure

Reinforcement-Driven Spread of Innovations and Fads

We propose kinetic models for the spread of permanent innovations and transient fads by the mechanism of social reinforcement. Each individual can be in one of M+1 states of awareness 0,1,2,...,M, with state M corresponding to adopting an innovation. An individual with awareness k<M increases to k+1 by interacting with an adopter. Starting with a single adopter, the time for an initially unaware population of size N to adopt a permanent innovation grows as ln(N) for M=1, and as N^{1-1/M} for M>1. The fraction of the population that remains clueless about a transient fad after it has come and gone changes discontinuously as a function of the fad abandonment rate lambda for M>1. The fad dies out completely in a time that varies non-monotonically with lambda.Comment: 4 pages, 2 columns, 5 figures, revtex 4-1 format; revised version has been expanded and put into iop format, with one figure adde

Influence Diffusion in Social Networks under Time Window Constraints

We study a combinatorial model of the spread of influence in networks that generalizes existing schemata recently proposed in the literature. In our model, agents change behaviors/opinions on the basis of information collected from their neighbors in a time interval of bounded size whereas agents are assumed to have unbounded memory in previously studied scenarios. In our mathematical framework, one is given a network $G=(V,E)$, an integer value $t(v)$ for each node $v\in V$, and a time window size $\lambda$. The goal is to determine a small set of nodes (target set) that influences the whole graph. The spread of influence proceeds in rounds as follows: initially all nodes in the target set are influenced; subsequently, in each round, any uninfluenced node $v$ becomes influenced if the number of its neighbors that have been influenced in the previous $\lambda$ rounds is greater than or equal to $t(v)$. We prove that the problem of finding a minimum cardinality target set that influences the whole network $G$ is hard to approximate within a polylogarithmic factor. On the positive side, we design exact polynomial time algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared in: Proceedings of 20th International Colloquium on Structural Information and Communication Complexity (Sirocco 2013), Lectures Notes in Computer Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201

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

Dynamics in online social networks

An increasing number of today's social interactions occurs using online social media as communication channels. Some online social networks have become extremely popular in the last decade. They differ among themselves in the character of the service they provide to online users. For instance, Facebook can be seen mainly as a platform for keeping in touch with close friends and relatives, Twitter is used to propagate and receive news, LinkedIn facilitates the maintenance of professional contacts, Flickr gathers amateurs and professionals of photography, etc. Albeit different, all these online platforms share an ingredient that pervades all their applications. There exists an underlying social network that allows their users to keep in touch with each other and helps to engage them in common activities or interactions leading to a better fulfillment of the service's purposes. This is the reason why these platforms share a good number of functionalities, e.g., personal communication channels, broadcasted status updates, easy one-step information sharing, news feeds exposing broadcasted content, etc. As a result, online social networks are an interesting field to study an online social behavior that seems to be generic among the different online services. Since at the bottom of these services lays a network of declared relations and the basic interactions in these platforms tend to be pairwise, a natural methodology for studying these systems is provided by network science. In this chapter we describe some of the results of research studies on the structure, dynamics and social activity in online social networks. We present them in the interdisciplinary context of network science, sociological studies and computer science.Comment: 17 pages, 4 figures, book chapte

The Dynamics of Protest Recruitment through an Online Network

The recent wave of mobilizations in the Arab world and across Western countries has generated much discussion on how digital media is connected to the diffusion of protests. We examine that connection using data from the surge of mobilizations that took place in Spain in May 2011. We study recruitment patterns in the Twitter network and find evidence of social influence and complex contagion. We identify the network position of early participants (i.e. the leaders of the recruitment process) and of the users who acted as seeds of message cascades (i.e. the spreaders of information). We find that early participants cannot be characterized by a typical topological position but spreaders tend to be more central in the network. These findings shed light on the connection between online networks, social contagion, and collective dynamics, and offer an empirical test to the recruitment mechanisms theorized in formal models of collective action