Page 622 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 622
COMBINATORICS AND DISCRETE MATHEMATICS
Semirings and temporal network analysis
Vladimir Batagelj, vladimir.batagelj@fmf.uni-lj.si
IMFM, Ljubljana, Slovenia
A semiring is a "natural" structure to formalize computations with link weights in networks. In
a temporal network, the presence/activity and properties/weights of nodes and links can change
through time. To describe temporal networks we introduce the notion of temporal quantities.
We define the addition and multiplication of temporal quantities in a way that can be used for
the definition of addition and multiplication of temporal networks. The corresponding algebraic
structures are semirings. We developed fast algorithms for both operations [2]. Large networks
are usually sparse. We answer the question when the product of sparse networks is sparse itself
[1, 4]. The proposed approach enables us to treat as temporal quantities also other network char-
acteristics such as degrees, connectivity components, centrality measures, Pathfinder skeleton,
etc. It is supported by the Python library Nets [5].
As a special case, we present two ways (instantaneous and cumulative) to transform bib-
liographic networks, using the works’ publication year, into corresponding temporal networks
based on temporal quantities. We also show how to use the addition of temporal quantities to
define interesting temporal properties of nodes, links and their groups thus providing an insight
into the evolution of bibliographic networks. Using the multiplication of temporal networks
we obtain different derived temporal networks providing us with new views on studied net-
works [3].
The proposed approach is illustrated with examples from the analysis of Franzosi’s violence
network, Corman’s Reuters terror news network, and a collection of bibliographic networks
from WoS.
References
[1] Batagelj, V, Cerinšek, M: On bibliographic networks. Scientometrics 96 (2013) 3, 845-
864.
[2] Batagelj, V., Praprotnik, S.: An algebraic approach to temporal network analysis based on
temporal quantities. Social Network Analysis and Mining, 6 (2016) 1, 1-22.
[3] Batagelj, V, Maltseva, D: Temporal Bibliographic Networks. Journal of Informetrics, 14
(2020) 1, 101006.
[4] Batagelj, V: On Fractional Approach to Analysis of Linked Networks. Scientometrics
(2020) online.
[5] Batagelj, V: https://github.com/bavla/Nets
620
Semirings and temporal network analysis
Vladimir Batagelj, vladimir.batagelj@fmf.uni-lj.si
IMFM, Ljubljana, Slovenia
A semiring is a "natural" structure to formalize computations with link weights in networks. In
a temporal network, the presence/activity and properties/weights of nodes and links can change
through time. To describe temporal networks we introduce the notion of temporal quantities.
We define the addition and multiplication of temporal quantities in a way that can be used for
the definition of addition and multiplication of temporal networks. The corresponding algebraic
structures are semirings. We developed fast algorithms for both operations [2]. Large networks
are usually sparse. We answer the question when the product of sparse networks is sparse itself
[1, 4]. The proposed approach enables us to treat as temporal quantities also other network char-
acteristics such as degrees, connectivity components, centrality measures, Pathfinder skeleton,
etc. It is supported by the Python library Nets [5].
As a special case, we present two ways (instantaneous and cumulative) to transform bib-
liographic networks, using the works’ publication year, into corresponding temporal networks
based on temporal quantities. We also show how to use the addition of temporal quantities to
define interesting temporal properties of nodes, links and their groups thus providing an insight
into the evolution of bibliographic networks. Using the multiplication of temporal networks
we obtain different derived temporal networks providing us with new views on studied net-
works [3].
The proposed approach is illustrated with examples from the analysis of Franzosi’s violence
network, Corman’s Reuters terror news network, and a collection of bibliographic networks
from WoS.
References
[1] Batagelj, V, Cerinšek, M: On bibliographic networks. Scientometrics 96 (2013) 3, 845-
864.
[2] Batagelj, V., Praprotnik, S.: An algebraic approach to temporal network analysis based on
temporal quantities. Social Network Analysis and Mining, 6 (2016) 1, 1-22.
[3] Batagelj, V, Maltseva, D: Temporal Bibliographic Networks. Journal of Informetrics, 14
(2020) 1, 101006.
[4] Batagelj, V: On Fractional Approach to Analysis of Linked Networks. Scientometrics
(2020) online.
[5] Batagelj, V: https://github.com/bavla/Nets
620
