Graph Theory

4-Quasiperiodic Functions on Graphs and Hypergraphs by Rudenskaya O.G. PDF

By Rudenskaya O.G.

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07:00 11:00 13:00 17:00 19:15 21:00 07:00 07:00 14:00 19:00 . .. Fig. 2. Construction of the network between the various locations in the city of Portland as reported by Chowell et al. (2003). The table is a small sample of the data set, obtained through a TRANSIMS simulation, which records for each individual the successive locations visited during a day, with the arrival and departure time. The network between locations is constructed from this data set: an edge exists between location i and j whenever an individual has gone directly from i to j, and the weight wi j gives the daily traffic between i and j.

12) where the factor 3 is due to the fact that each triangle is associated with three nodes. This definition corresponds to the concept of the fraction of transitive triples introduced in sociology (Wasserman and Faust, 1994). Different definitions give rise to different values of the clustering coefficient for a given graph. Hence, the comparison of clustering coefficients among different graphs must use the very same measure. In any case, both measures are normalized and bounded to be between 0 and 1.

2 This project has been running since 1997 and is one of the first projects to provide regular snapshots of the Internet’s evolution. , 2002b). All the data are then centrally collected and merged in order to obtain large-scale Internet maps that minimize measurement biases. A different active strategy, the Distributed Internet Measurements and Simulations (DIMES) project (Shavitt and Shir, 2005), considers a distributed measurement infrastructure, based on the deployment of thousands of lightweight measurement agents around the globe.

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4-Quasiperiodic Functions on Graphs and Hypergraphs by Rudenskaya O.G.

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