19 research outputs found
Random Majority Opinion Diffusion: Stabilization Time, Absorbing States, and Influential Nodes
Consider a graph G with n nodes and m edges, which represents a social
network, and assume that initially each node is blue or white. In each round,
all nodes simultaneously update their color to the most frequent color in their
neighborhood. This is called the Majority Model (MM) if a node keeps its color
in case of a tie and the Random Majority Model (RMM) if it chooses blue with
probability 1/2 and white otherwise.
We prove that there are graphs for which RMM needs exponentially many rounds
to reach a stable configuration in expectation, and such a configuration can
have exponentially many states (i.e., colorings). This is in contrast to MM,
which is known to always reach a stable configuration with one or two states in
rounds. For the special case of a cycle graph C_n, we prove the stronger
and tight bounds of and in MM and RMM,
respectively. Furthermore, we show that the number of stable colorings in MM on
C_n is equal to , where is the golden
ratio, while it is equal to 2 for RMM.
We also study the minimum size of a winning set, which is a set of nodes
whose agreement on a color in the initial coloring enforces the process to end
in a coloring where all nodes share that color. We present tight bounds on the
minimum size of a winning set for both MM and RMM.
Furthermore, we analyze our models for a random initial coloring, where each
node is colored blue independently with some probability and white
otherwise. Using some martingale analysis and counting arguments, we prove that
the expected final number of blue nodes is respectively equal to
and pn in MM and RMM on a cycle graph C_n.
Finally, we conduct some experiments which complement our theoretical
findings and also lead to the proposal of some intriguing open problems and
conjectures to be tackled in future work.Comment: Accepted in AAMAS 2023 (The 22nd International Conference on
Autonomous Agents and Multiagent Systems
Two Phase Transitions in Two-Way Bootstrap Percolation
Consider a graph G and an initial random configuration, where each node is black with probability p and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least r black neighbors and white otherwise. We prove that this basic process exhibits a threshold behavior with two phase transitions when the underlying graph is a d-dimensional torus and identify the threshold values
Mitigating Misinformation Spreading in Social Networks Via Edge Blocking
The wide adoption of social media platforms has brought about numerous
benefits for communication and information sharing. However, it has also led to
the rapid spread of misinformation, causing significant harm to individuals,
communities, and society at large. Consequently, there has been a growing
interest in devising efficient and effective strategies to contain the spread
of misinformation. One popular countermeasure is blocking edges in the
underlying network.
We model the spread of misinformation using the classical Independent Cascade
model and study the problem of minimizing the spread by blocking a given number
of edges. We prove that this problem is computationally hard, but we propose an
intuitive community-based algorithm, which aims to detect well-connected
communities in the network and disconnect the inter-community edges. Our
experiments on various real-world social networks demonstrate that the proposed
algorithm significantly outperforms the prior methods, which mostly rely on
centrality measures