Topologically biased random walk and community finding in networks.
نویسندگان
چکیده
We present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities.
منابع مشابه
Sampling from social networks’s graph based on topological properties and bee colony algorithm
In recent years, the sampling problem in massive graphs of social networks has attracted much attention for fast analyzing a small and good sample instead of a huge network. Many algorithms have been proposed for sampling of social network’ graph. The purpose of these algorithms is to create a sample that is approximately similar to the original network’s graph in terms of properties such as de...
متن کاملLine crossing problem for biased monotonic random walks in the plane
In this paper, we study the problem of finding the probability that the two-dimensional (biased) monotonic random walk crosses the line y = αx+d, where α, d ≥ 0. A β-biased monotonic random walk moves from (a, b) to (a + 1, b) or (a, b + 1) with probabilities 1/(β + 1) and β/(β + 1), respectively. Among our results, we show that if β ≥ ⌈α⌉, then the β-biased monotonic random walk, starting from...
متن کاملRandom Walk on Periodic Treeschristiane Takacs
Following Lyons (1990, 4]) we deene a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric networks. 1. Introduction This paper deals ...
متن کاملRandom Walk on Periodic Trees
Following Lyons (1990, [4]) we define a periodic tree, restate its branching number and consider a biased random walk on it. In the case of a transient walk, we describe the walk-invariant random periodic tree and calculate the asymptotic rate of escape (speed) of the walk. This is achieved by exploiting the connections between random walks and electric networks.
متن کاملCore-biased random walks in complex networks
A simple strategy to explore a network is to use a random-walk where the walker jumps from one node to an adjacent node at random. It is known that biasing the random jump, the walker can explore every walk of the same length with equal probability, this is known as a Maximal Entropy Random Walk (MERW). To construct a MERW requires the knowledge of the largest eigenvalue Λ and corresponding eig...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E, Statistical, nonlinear, and soft matter physics
دوره 82 6 Pt 2 شماره
صفحات -
تاریخ انتشار 2010