  In a temporal network, the presence and activity 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. The usual approach to (data) analysis of temporal networks is to
transform it into a sequence of time slices -- static networks corresponding to
selected time intervals and analyze each of them using standard methods to
produce a sequence of results. The approach proposed in this paper enables us
to compute these results directly. We developed fast algorithms for the
proposed operations. They are available as an open source Python library TQ
(Temporal Quantities) and a program Ianus. The proposed approach enables us to
treat as temporal quantities also other network characteristics such as
degrees, connectivity components, centrality measures, Pathfinder skeleton,
etc. To illustrate the developed tools we present some results from the
analysis of Franzosi's violence network and Corman's Reuters terror news
network.
