4,121 research outputs found
On the convergence of message passing computation of harmonic influence in social networks
International audienceThe harmonic influence is a measure of node influence in social networks that quantifies the ability of a leader node to alter the average opinion of the network, acting against an adversary field node. The definition of harmonic influence assumes linear interactions between the nodes described by an undirected weighted graph; its computation is equivalent to solve a discrete Dirichlet problem associated to a grounded Laplacian for every node. This measure has been recently studied, under slightly more restrictive assumptions, by Vassio et al., IEEE Trans. Control Netw. Syst., 2014, who proposed a distributed message passing algorithm that concurrently computes the harmonic influence of all nodes. In this paper, we provide a convergence analysis for this algorithm, which largely extends upon previous results: we prove that the algorithm converges asymptotically, under the only assumption of the interaction Laplacian being symmetric. However, the convergence value does not in general coincide with the harmonic influence: by simulations, we show that when the network has a larger number of cycles, the algorithm becomes slower and less accurate, but nevertheless provides a useful approximation. Simulations also indicate that the symmetry condition is not necessary for convergence and that performance scales very well in the number of nodes of the graph
Effects of Network Communities and Topology Changes in Message-Passing Computation of Harmonic Influence in Social Networks
The harmonic influence is a measure of the importance of nodes in social
networks, which can be approximately computed by a distributed message-passing
algorithm. In this extended abstract we look at two open questions about this
algorithm. How does it perform on real social networks, which have complex
topologies structured in communities? How does it perform when the network
topology changes while the algorithm is running? We answer these two questions
by numerical experiments on a Facebook ego network and on synthetic networks,
respectively. We find out that communities can introduce artefacts in the final
approximation and cause the algorithm to overestimate the importance of "local
leaders" within communities. We also observe that the algorithm is able to
adapt smoothly to changes in the topology.Comment: 4 pages, 7 figures, submitted as conference extended abstrac
Message passing optimization of Harmonic Influence Centrality
This paper proposes a new measure of node centrality in social networks, the
Harmonic Influence Centrality, which emerges naturally in the study of social
influence over networks. Using an intuitive analogy between social and
electrical networks, we introduce a distributed message passing algorithm to
compute the Harmonic Influence Centrality of each node. Although its design is
based on theoretical results which assume the network to have no cycle, the
algorithm can also be successfully applied on general graphs.Comment: 11 pages; 10 figures; to appear as a journal publicatio
Optimizing Opinions with Stubborn Agents
We consider the problem of optimizing the placement of stubborn agents in a
social network in order to maximally influence the population. We assume the
network contains stubborn users whose opinions do not change, and non-stubborn
users who can be persuaded. We further assume the opinions in the network are
in an equilibrium that is common to many opinion dynamics models, including the
well-known DeGroot model.
We develop a discrete optimization formulation for the problem of maximally
shifting the equilibrium opinions in a network by targeting users with stubborn
agents. The opinion objective functions we consider are the opinion mean, the
opinion variance, and the number of individuals whose opinion exceeds a fixed
threshold. We show that the mean opinion is a monotone submodular function,
allowing us to find a good solution using a greedy algorithm. We find that on
real social networks in Twitter consisting of tens of thousands of individuals,
a small number of stubborn agents can non-trivially influence the equilibrium
opinions. Furthermore, we show that our greedy algorithm outperforms several
common benchmarks.
We then propose an opinion dynamics model where users communicate noisy
versions of their opinions, communications are random, users grow more stubborn
with time, and there is heterogeneity is how users' stubbornness increases. We
prove that under fairly general conditions on the stubbornness rates of the
individuals, the opinions in this model converge to the same equilibrium as the
DeGroot model, despite the randomness and user heterogeneity in the model.Comment: 40 pages, 11 figure
Distributed estimation and control of node centrality in undirected asymmetric networks
Measures of node centrality that describe the importance of a node within a
network are crucial for understanding the behavior of social networks and
graphs. In this paper, we address the problems of distributed estimation and
control of node centrality in undirected graphs with asymmetric weight values.
In particular, we focus our attention on -centrality, which can be seen
as a generalization of eigenvector centrality. In this setting, we first
consider a distributed protocol where agents compute their -centrality,
focusing on the convergence properties of the method; then, we combine the
estimation method with a consensus algorithm to achieve a consensus value
weighted by the influence of each node in the network. Finally, we formulate an
-centrality control problem which is naturally decoupled and, thus,
suitable for a distributed setting and we apply this formulation to protect the
most valuable nodes in a network against a targeted attack, by making every
node in the network equally important in terms of {\alpha}-centrality.
Simulations results are provided to corroborate the theoretical findings.Comment: published on IEEE Transactions on Automatic Control
https://ieeexplore.ieee.org/abstract/document/912618
Effects of Network Communities and Topology Changes in Message-Passing Computation of Harmonic Influence in Social Networks
International audienceThe harmonic influence is a measure of the importance of nodes in social networks, which can be approximately computed by a distributed message-passing algorithm. In this extended abstract we look at two open questions about this algorithm. How does it perform on real social networks, which have complex topologies structured in communities? How does it perform when the network topology changes while the algorithm is running? We answer these two questions by numerical experiments on a Facebook ego network and on synthetic networks, respectively. We find out that communities can introduce artefacts in the final approximation and cause the algorithm to overestimate the importance of "local leaders" within communities. We also observe that the algorithm is able to adapt smoothly to changes in the topology
Mean-field analysis of the convergence time of message-passing computation of harmonic influence in social networks
International audienceThe concept of harmonic influence has been recently proposed as a metric for the importance of nodes in a social network. A distributed message passing algorithm for its computation has been proposed by Vassio et al. (2014) and proved to converge on general graphs by Rossi and Frasca (2016a). In this paper, we want to evaluate the convergence time of this algorithm by using a mean-field approach. The mean-field dynamics is first introduced in a homogeneous setting, where it is exact, then heuristically extended to a non-homogeneous setting. The rigorous analysis of the mean-field dynamics is complemented by numerical examples and simulations that demonstrate the validity of the approach
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