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 - 2015
Externally published	Yes
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

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

Funding

Supported in part by the Israel Science Foundation (grant 1549/13).

Funders	Funder number
Israel Science Foundation
Israel Science Foundation	1549/13

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)).

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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

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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.

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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

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