Graph Theory and Its Applications

Gross, Jonathan L.; Yellen, Jay; Anderson, Mark

doi:10.1201/9780429425134

Cited by 261 publications

(245 citation statements)

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“…According to graph theory (Gross & Yellen, ; Minor & Urban, ), the junction of any two rivers and the starting and terminal points of any one river are considered nodes. A river reach segmented by any two nodes is considered an edge.…”

Section: Discussionmentioning

confidence: 99%

Impacts of human activities on the structural and functional connectivity of a river network in the Taihu Plain

Deng

Han

2018

Land Degrad Dev

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Human activities are expected to change the hydrological connectivity of river networks. Understanding the impacts of human activities on hydrological connectivity is crucial for river‐basin management. The present study investigated the impacts of river network change and water gate construction on the structural and functional connectivity in the Taihu Plain. We found that the network circuitry, edge‐node ratio, and network connectivity of the arterial river network increased by 8.82%, 3.59%, and 3.57%, respectively, during the 1960s–2010s. In Jiangyin, the indexes decreased by 46.40%, 15.43%, and 15.42%, respectively, throughout the river network during the 1960s–1980s. The indexes of the capillary river network decreased by 61.90%, 24.89%, and 24.88%, respectively, while those of the arterial river network increased by 6.58%, 4.73%, and 2.72%, respectively. We also found that the current longitudinal continuity of the river network was 8.15. In the Sangan River of Zhangjiagang, the migratory continuity of the river network was 0.27, but it was between 0.33 and 1.00 when the current water gates were considered separately, and the decreases of their maximum values under different combinations were greater than those of their minimum values. Moreover, we found that the various water levels of the river network all exhibited increasing trends, and their correlations with functional connectivity were significant and positive. Our study suggests that the negative effects of river network changes on structural connectivity were far greater than the positive effects, and the impacts of water gate construction on functional connectivity had gradient and cumulative effects.

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Section: Discussionmentioning

confidence: 99%

Impacts of human activities on the structural and functional connectivity of a river network in the Taihu Plain

Deng

Han

2018

Land Degrad Dev

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“…The proof of Lemma 9 follows a similar line of the argument as the Hall's Theorem [28]. The complete proof using the min-cut max-flow theorem is provided in [20].…”

Section: A Performance Analysismentioning

confidence: 94%

The Streaming Capacity of Sparsely Connected P2P Systems With Distributed Control

Zhao

Lin

2016

IEEE/ACM Trans. Networking

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Peer-to-peer (P2P) streaming technologies can take advantage of the upload capacity of clients, and hence can scale to large content distribution networks with lower cost. A fundamental question for P2P streaming systems is the maximum streaming rate that all users can sustain. Prior works have studied the optimal streaming rate for a complete network, where every peer is assumed to be able to communicate with all other peers. This is, however, an impractical assumption in real systems. In this paper, we are interested in the achievable streaming rate when each peer can only connect to a small number of neighbors. We show that even with a random peer-selection algorithm and uniform rate allocation, as long as each peer maintains downstream neighbors, where is the total number of peers in the system, the system can asymptotically achieve a streaming rate that is close to the optimal streaming rate of a complete network. These results reveal a number of important insights into the dynamics of the system, based on which we then design simple improved algorithms that can reduce the constant factor in front of the term, yet can achieve the same level of performance guarantee. Simulation results are provided to verify our analysis.Index Terms-Distributed control, live streaming, peer-to-peer (P2P) networks, sparse connectivity, streaming capacity.

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“…Our graph theory notations and terminology are standard and can be found in all graph theory books, like [4,6,8]. If x, y are vertices of the digraph G, then a path in G from x to y of length n (n ∈ N) is a sequence (x i ) n i=0 of n + 1 vertices such that x 0 = x, x n = y and…”

Section: Definition 213mentioning

confidence: 99%