Core size and densification in preferential attachment networks

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Consider a preferential attachment model for network evolution that allows both node and edge arrival events: at time t, with probability pt a new node arrives and a new edge is added between the new node and an existing node, and with probability 1 - pt a new edge is added between two existing nodes. In both cases existing nodes are chosen at random according to preferential attachment, i.e., with probability proportional to their degree. For δ ∈ (0, 1), the δ-founders of the network at time t is the minimal set of the first nodes to enter the network (i.e., founders) guaranteeing that the sum of degrees of nodes in the set is at least a δ fraction of the number of edges in the graph at time t. We show that for the common model where pt is constant, i.e., when pt = p for every t and the network is sparse with linear number of edges, the size of the δ-founders set is concentrated around δ2/pnt, and thus is linear in nt, the number of nodes at time t.

Original languageAmerican English
Title of host publicationAutomata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
EditorsNaoki Kobayashi, Bettina Speckmann, Kazuo Iwama, Magnus M. Halldorsson
PublisherSpringer Verlag
Pages492-503
Number of pages12
ISBN (Print)9783662476659
DOIs
StatePublished - 1 Jan 2015
Event42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan
Duration: 6 Jul 201510 Jul 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9135

Conference

Conference42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
Country/TerritoryJapan
CityKyoto
Period6/07/1510/07/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

Fingerprint

Dive into the research topics of 'Core size and densification in preferential attachment networks'. Together they form a unique fingerprint.

Cite this