Tracking Clustering Coefficient on Dynamic Graph via Incremental Random Walk

Lecture Notes in Computer Science - Web Information Systems Engineering – WISE 2017 ◽

10.1007/978-3-319-68783-4_33 ◽

2017 ◽

pp. 488-496

Author(s):

Qun Liao ◽

Lei Sun ◽

Yunpeng Yuan ◽

Yulu Yang

Keyword(s):

Random Walk ◽

Clustering Coefficient ◽

Dynamic Graph

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An Incremental Algorithm for Estimating Average Clustering Coefficient Based on Random Walk

Web and Big Data - Lecture Notes in Computer Science ◽

10.1007/978-3-319-63579-8_13 ◽

2017 ◽

pp. 158-165

Author(s):

Qun Liao ◽

Lei Sun ◽

He Du ◽

Yulu Yang

Keyword(s):

Random Walk ◽

Clustering Coefficient ◽

Incremental Algorithm

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Estimating Clustering Coefficient via Random Walk on MapReduce

2017 IEEE 23rd International Conference on Parallel and Distributed Systems (ICPADS) ◽

10.1109/icpads.2017.00071 ◽

2017 ◽

Cited By ~ 1

Author(s):

Qun Liao ◽

Yulu Yang

Keyword(s):

Random Walk ◽

Clustering Coefficient

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Cover Time in Edge-Uniform Stochastically-Evolving Graphs

Algorithms ◽

10.3390/a11100149 ◽

2018 ◽

Vol 11 (10) ◽

pp. 149 ◽

Cited By ~ 2

Author(s):

Ioannis Lamprou ◽

Russell Martin ◽

Paul Spirakis

Keyword(s):

Random Walk ◽

Single Agent ◽

Simple Random Walk ◽

Electrical Network ◽

Dynamic Graph ◽

Cover Time ◽

Time Step ◽

Evolving Graphs ◽

Expected Time ◽

Experimental Findings

We define a general model of stochastically-evolving graphs, namely the edge-uniform stochastically-evolving graphs. In this model, each possible edge of an underlying general static graph evolves independently being either alive or dead at each discrete time step of evolution following a (Markovian) stochastic rule. The stochastic rule is identical for each possible edge and may depend on the past k ≥ 0 observations of the edge’s state. We examine two kinds of random walks for a single agent taking place in such a dynamic graph: (i) The Random Walk with a Delay (RWD), where at each step, the agent chooses (uniformly at random) an incident possible edge, i.e., an incident edge in the underlying static graph, and then, it waits till the edge becomes alive to traverse it. (ii) The more natural Random Walk on what is Available (RWA), where the agent only looks at alive incident edges at each time step and traverses one of them uniformly at random. Our study is on bounding the cover time, i.e., the expected time until each node is visited at least once by the agent. For RWD, we provide a first upper bound for the cases k = 0 , 1 by correlating RWD with a simple random walk on a static graph. Moreover, we present a modified electrical network theory capturing the k = 0 case. For RWA, we derive some first bounds for the case k = 0 , by reducing RWA to an RWD-equivalent walk with a modified delay. Further, we also provide a framework that is shown to compute the exact value of the cover time for a general family of stochastically-evolving graphs in exponential time. Finally, we conduct experiments on the cover time of RWA in edge-uniform graphs and compare the experimental findings with our theoretical bounds.

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