Core size and densification in preferential attachment networks

Chen Avin; Zvi Lotker; Yinon Nahum; David Peleg

doi:10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks

Chen Avin, Zvi Lotker, Yinon Nahum, David Peleg

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Scopus citations

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 - p_t 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 p_t is constant, i.e., when p_t = 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/^pn_t, and thus is linear in n_t, the number of nodes at time t.

Original language	English
Title of host publication	Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings
Editors	Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama, Magnus M. Halldorsson
Publisher	Springer Verlag
Pages	492-503
Number of pages	12
ISBN (Print)	9783662476659
DOIs	https://doi.org/10.1007/978-3-662-47666-6_39
State	Published - 1 Jan 2015
Event	42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan Duration: 6 Jul 2015 → 10 Jul 2015

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9135
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	42nd International Colloquium on Automata, Languages and Programming, ICALP 2015
Country/Territory	Japan
City	Kyoto
Period	6/07/15 → 10/07/15

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-662-47666-6_39

Cite this

Avin, C., Lotker, Z., Nahum, Y., & Peleg, D. (2015). Core size and densification in preferential attachment networks. In N. Kobayashi, B. Speckmann, K. Iwama, & M. M. Halldorsson (Eds.), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings (pp. 492-503). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9135). Springer Verlag. https://doi.org/10.1007/978-3-662-47666-6_39

Avin, Chen ; Lotker, Zvi ; Nahum, Yinon et al. / Core size and densification in preferential attachment networks. Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. editor / Naoki Kobayashi ; Bettina Speckmann ; Kazuo Iwama ; Magnus M. Halldorsson. Springer Verlag, 2015. pp. 492-503 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{1973786e118146019d4f27fdc2ad6a05,

title = "Core size and densification in preferential attachment networks",

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.",

author = "Chen Avin and Zvi Lotker and Yinon Nahum and David Peleg",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2015.; 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 ; Conference date: 06-07-2015 Through 10-07-2015",

year = "2015",

month = jan,

day = "1",

doi = "10.1007/978-3-662-47666-6_39",

language = "English",

isbn = "9783662476659",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "492--503",

editor = "Naoki Kobayashi and Bettina Speckmann and Kazuo Iwama and Halldorsson, {Magnus M.}",

booktitle = "Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings",

address = "Germany",

}

Avin, C, Lotker, Z, Nahum, Y & Peleg, D 2015, Core size and densification in preferential attachment networks. in N Kobayashi, B Speckmann, K Iwama & MM Halldorsson (eds), Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9135, Springer Verlag, pp. 492-503, 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015, Kyoto, Japan, 6/07/15. https://doi.org/10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks. / Avin, Chen; Lotker, Zvi; Nahum, Yinon et al.
Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. ed. / Naoki Kobayashi; Bettina Speckmann; Kazuo Iwama; Magnus M. Halldorsson. Springer Verlag, 2015. p. 492-503 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9135).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Core size and densification in preferential attachment networks

AU - Avin, Chen

AU - Lotker, Zvi

AU - Nahum, Yinon

AU - Peleg, David

N1 - Publisher Copyright: © Springer-Verlag Berlin Heidelberg 2015.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84950136198&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-47666-6_39

DO - 10.1007/978-3-662-47666-6_39

M3 - Conference contribution

AN - SCOPUS:84950136198

SN - 9783662476659

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 492

EP - 503

BT - Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings

A2 - Kobayashi, Naoki

A2 - Speckmann, Bettina

A2 - Iwama, Kazuo

A2 - Halldorsson, Magnus M.

PB - Springer Verlag

T2 - 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015

Y2 - 6 July 2015 through 10 July 2015

ER -

Avin C, Lotker Z, Nahum Y, Peleg D. Core size and densification in preferential attachment networks. In Kobayashi N, Speckmann B, Iwama K, Halldorsson MM, editors, Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. Springer Verlag. 2015. p. 492-503. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-662-47666-6_39

Core size and densification in preferential attachment networks

Abstract

Publication series

Conference

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this