Joint Distribution of Distances in Large Random Regular Networks

Joint distribution of distances in random regular networks

We study the array of point-to-point distances in random regular graphs equipped with exponential edge-lengths. We consider the regime where the degree is kept fixed while the number of vertices tends to infinity. The marginal distribution of an individual entry is now well-understood, thanks to the work of Bhamidi, van der Hofstad and Hooghiemstra (2010). The purpose of this note is to show th...

fault location in power distribution networks using matching algorithm

چکیده رساله/پایان نامه : تاکنون روش‏های متعددی در ارتباط با مکان یابی خطا در شبکه انتقال ارائه شده است. استفاده مستقیم از این روش‏ها در شبکه توزیع به دلایلی همچون وجود انشعاب‏های متعدد، غیر یکنواختی فیدرها (خطوط کابلی، خطوط هوایی، سطح مقطع متفاوت انشعاب ها و تنه اصلی فیدر)، نامتعادلی (عدم جابجا شدگی خطوط، بارهای تک‏فاز و سه فاز)، ثابت نبودن بار و اندازه گیری مقادیر ولتاژ و جریان فقط در ابتدای...

Distances in random Apollonian networks

Typical Distances in Ultrasmall Random Networks

We show that in preferential attachment models with power-law exponent τ ∈ (2, 3) the distance between randomly chosen vertices in the giant component is asymptotically equal to (4 + o(1)) log logN − log(τ−2) , where N denotes the number of nodes. This is twice the value obtained for the configuration model with the same power-law exponent. The extra factor reveals the different structure of ty...

Distribution of subgraphs of random regular graphs

The asymptotic distribution of small subgraphs of a random graph has been basically worked out (see Ruciński [5] for example). But for random regular graphs, the main techniques for proving, for instance, asymptotic normality, do not seem to be usable. One very recent result in this direction is to be found in [3], where switchings were applied to cycle counts. The aim of the present note is to...