Collective influence in evolutionary social dilemmas

When evolutionary games are contested in structured populations, the degree of each player in the network plays an important role. If they exist, hubs often determine the fate of the population in remarkable ways. Recent research based on optimal percolation in random networks has shown, however, that the degree is neither the sole nor the best predictor of influence in complex networks. Low-degree nodes may also be optimal influencers if they are hierarchically linked to hubs. Taking this into account leads to the formalism of collective influence in complex networks, which as we show here, has far-reaching implications for the favorable resolution of social dilemmas. In particular, there exists an optimal hierarchical depth for the determination of collective influence that we use to describe the potency of players for passing their strategies, which depends on the strength of the social dilemma. Interestingly, the degree, which corresponds to the baseline depth zero, is optimal only when the temptation to defect is small. Our research reveals that evolutionary success stories are related to spreading processes which are rooted in favorable hierarchical structures that extend beyond local neighborhoods.Comment: 6 pages, 5 figures; accepted for publication in Europhysics Letter

How to Network in Online Social Networks

In this paper, we consider how to maximize users' influence in Online Social Networks (OSNs) by exploiting social relationships only. Our first contribution is to extend to OSNs the model of Kempe et al. [1] on the propagation of information in a social network and to show that a greedy algorithm is a good approximation of the optimal algorithm that is NP-hard. However, the greedy algorithm requires global knowledge, which is hardly practical. Our second contribution is to show on simulations on the full Twitter social graph that simple and practical strategies perform close to the greedy algorithm.Comment: NetSciCom 2014 - The Sixth IEEE International Workshop on Network Science for Communication Networks (2014

Optimal percolation on multiplex networks

Optimal percolation is the problem of finding the minimal set of nodes such that if the members of this set are removed from a network, the network is fragmented into non-extensive disconnected clusters. The solution of the optimal percolation problem has direct applicability in strategies of immunization in disease spreading processes, and influence maximization for certain classes of opinion dynamical models. In this paper, we consider the problem of optimal percolation on multiplex networks. The multiplex scenario serves to realistically model various technological, biological, and social networks. We find that the multilayer nature of these systems, and more precisely multiplex characteristics such as edge overlap and interlayer degree-degree correlation, profoundly changes the properties of the set of nodes identified as the solution of the optimal percolation problem.Comment: 7 pages, 5 figures + appendi

Searching for superspreaders of information in real-world social media

A number of predictors have been suggested to detect the most influential spreaders of information in online social media across various domains such as Twitter or Facebook. In particular, degree, PageRank, k-core and other centralities have been adopted to rank the spreading capability of users in information dissemination media. So far, validation of the proposed predictors has been done by simulating the spreading dynamics rather than following real information flow in social networks. Consequently, only model-dependent contradictory results have been achieved so far for the best predictor. Here, we address this issue directly. We search for influential spreaders by following the real spreading dynamics in a wide range of networks. We find that the widely-used degree and PageRank fail in ranking users' influence. We find that the best spreaders are consistently located in the k-core across dissimilar social platforms such as Twitter, Facebook, Livejournal and scientific publishing in the American Physical Society. Furthermore, when the complete global network structure is unavailable, we find that the sum of the nearest neighbors' degree is a reliable local proxy for user's influence. Our analysis provides practical instructions for optimal design of strategies for "viral" information dissemination in relevant applications.Comment: 12 pages, 7 figure

Effects of Time Horizons on Influence Maximization in the Voter Dynamics

In this paper we analyze influence maximization in the voter model with an active strategic and a passive influencing party in non-stationary settings. We thus explore the dependence of optimal influence allocation on the time horizons of the strategic influencer. We find that on undirected heterogeneous networks, for short time horizons, influence is maximized when targeting low-degree nodes, while for long time horizons influence maximization is achieved when controlling hub nodes. Furthermore, we show that for short and intermediate time scales influence maximization can exploit knowledge of (transient) opinion configurations. More in detail, we find two rules. First, nodes with states differing from the strategic influencer's goal should be targeted. Second, if only few nodes are initially aligned with the strategic influencer, nodes subject to opposing influence should be avoided, but when many nodes are aligned, an optimal influencer should shadow opposing influence.Comment: 22 page

Optimal Multiphase Investment Strategies for Influencing Opinions in a Social Network

We study the problem of optimally investing in nodes of a social network in a competitive setting, where two camps aim to maximize adoption of their opinions by the population. In particular, we consider the possibility of campaigning in multiple phases, where the final opinion of a node in a phase acts as its initial biased opinion for the following phase. Using an extension of the popular DeGroot-Friedkin model, we formulate the utility functions of the camps, and show that they involve what can be interpreted as multiphase Katz centrality. Focusing on two phases, we analytically derive Nash equilibrium investment strategies, and the extent of loss that a camp would incur if it acted myopically. Our simulation study affirms that nodes attributing higher weightage to initial biases necessitate higher investment in the first phase, so as to influence these biases for the terminal phase. We then study the setting in which a camp's influence on a node depends on its initial bias. For single camp, we present a polynomial time algorithm for determining an optimal way to split the budget between the two phases. For competing camps, we show the existence of Nash equilibria under reasonable assumptions, and that they can be computed in polynomial time