Community Recovery in a Preferential Attachment Graph
A message passing algorithm is derived for recovering communities within a graph generated by a variation of the Barab\'{a}si-Albert preferential attachment model. The estimator is assumed to know the arrival times, or order of attachment, of the vertices. The derivation of the algorithm is based on belief propagation under an independence assumption. Two precursors to the message passing algorithm are analyzed: the first is a degree thresholding (DT) algorithm and the second is an algorithm based on the arrival times of the children (C) of a given vertex, where the children of a given vertex are the vertices that attached to it. Comparison of the performance of the algorithms shows it is beneficial to know the arrival times, not just the number, of the children. The probability of correct classification of a vertex is asymptotically determined by the fraction of vertices arriving before it. Two extensions of Algorithm C are given: the first is based on joint likelihood of the children of a fixed set of vertices; it can sometimes be used to seed the message passing algorithm. The second is the message passing algorithm. Simulation results are given.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Information-theoretic Limits for Community Detection in Network Models
We analyze the information-theoretic limits for the recovery of node labels in several network models. This includes the Stochastic Block Model, the Exponential Random Graph Model, the Latent Space Model, the Directed Pr…
Community DetectionStochastic Block ModelPreferential Attachment Graphs with Planted Communities
A variation of the preferential attachment random graph model of Barab\'asi and Albert is defined that incorporates planted communities. The graph is built progressively, with new vertices attaching to the existing ones …
Growth Dynamics of Value and Cost Trade-off in Temporal Networks
The question is: What does happen to the real-world networks which cause them not to grow permanently? The idea here is that real-world networks have to pay the cost of growth. We investigate the growth and trade-off bet…
Networked Inequality: Preferential Attachment Bias in Graph Neural Network Link Prediction
Graph neural network (GNN) link prediction is increasingly deployed in citation, collaboration, and online social networks to recommend academic literature, collaborators, and friends. While prior research has investigat…
FairnessGraph Neural NetworkLink PredictionPredictionPower Law in Sparsified Deep Neural Networks
The power law has been observed in the degree distributions of many biological neural networks. Sparse deep neural networks, which learn an economical representation from the data, resemble biological neural networks in …
Continual Learning