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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Biased random walk on a graph ： ウィキペディア英語版 Biased random walk on a graph In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various potential new states; unlike in a pure random walk, the probabilities of the potential new states are unequal. Biased random walks on a graph provide an approach for the (structural analysis ) of undirected graphs in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by statistical methods. The concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and social networks. ==Model == There have been written many different representations of the biased random walks on graphs based on the particular purpose of the analysis. A common representation of the mechanism for undirected graphs is as follows: On an undirected graph, a walker takes a step from the current node, $j$, to node $i$. Assuming that each node has an attribute $\backslash alpha\_i$, the probability of jumping from node$j$ to $i$ is given by: $$ T_^\alpha=\tfrac \alpha_k A_} , where $A\_$ represents the topological weight of the edge going from $j$ to $i$. In fact, the steps of the walker are biased by the factor of $\backslash alpha$ which may differ from one node to another. Depending on the network, the attribute $\backslash alpha$ can be interpreted differently. It might be implied as the attraction of a person in a social network, it might be betweenness centrality or even it might be explained as an intrinsic characteristic of a node. It is obvious that in case of a (fair random walk on graph )$\backslash alpha$ is one for all the nodes. In case of shortest paths random walks $\backslash alpha\_i$ is the total number of the shortest paths between all pairs of nodes that pass through the node $i$. In fact the walker prefers the nodes with higher betweenness centrality which is defined as below: $$ C(i)=\tfrac} Based on the above equation, the recurrence time to a node in the biased walk is given by: $$ r_i=\tfrac 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Biased random walk on a graph」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.