TQ User guide


In a temporal network, the presence and activity of nodes and links can change through time. In the last two decades the interest for the analysis of temporal networks increased partially motivated by travel-support services and the analysis of sequences of interaction events (e-mails, news, phone calls, collaboration, etc.). The approaches and results were recently surveyed by Holme and Saramäki in their paper \citep{TNsur} and the book \citep{TNbook}.

Most of temporal social networks data contain the information about activity time intervals of their links, sometimes augmented by the activity intensity. The usual approach to the (data) analysis of temporal networks is to transform it into a sequence of time slices - static networks corresponding to selected time intervals - see for example \cite{DNvis,trends,elDyn}. Afterward each time slice is analyzed using the standard methods for analysis of static networks. Finally the results are collected into a temporal sequence of results. In this paper we propose an alternative approach, based on the notion of temporal quantity, that bypasses explicit construction of time slices. The developed algorithms are transforming temporal networks directly into results in the form of temporal quantities, vectors, temporal vectors or partitions, and temporal networks.

This user guide is based on the paper ArXiv. Most details about the algorithms and their background are omitted, and additional examples of applications of routines from the TQ library are included. In the paper, we first present the basic notions about temporal networks. In Section~\ref{secTQ} we introduce the temporal quantities and propose an algebraic approach, based on semirings, to the analysis of temporal networks. In the following sections we show that most of the traditional network analysis concepts and algorithms such as degrees, clustering coefficient, closeness, betweenness, weak and strong connectivity, PathFinder skeleton, etc. can be straightforwardly extended to their temporal versions.

Description of temporal networks

For the description of temporal networks we propose an elaborated version of the approach used in Pajek \citep{ESNA}. In our approach we also consider values of links (in most cases measuring the intensity/frequency of the activity). Pajek supports two types of descriptions of temporal networks based on presence and on events (Pajek 0.47, July 1999). Here, we will describe only the approach to capturing the presence of nodes and links.

A temporal network N =(V, L, T, P, W) is obtained by attaching the time, T, to an ordinary network, where T is a set of time points, t ∈ T. V is the set of nodes, L is the set of links, P is the set of node properties, and W is the set of link properties or weights \citep{ency}. The time T is usually either a subset of integers, T ⊆ ℤ, or a subset of reals, T ⊆ ℝ. In Pajek T ⊆ ℕ. In a general setting it could be any linearly ordered set.

In a temporal network, nodes v ∈ V and links e ∈ L are not necessarily present or active at all time points. Let T(v), T ∈ P, be the activity set of time points for the node v; and T(e), T ∈ W, the activity set of time points for the link e. The following consistency condition is imposed:

If a link e(u,v) is active at the time point t then its end-nodes u and v should be active at the time t. Formally we express this by T(e(u,v)) ⊆ T(u) ⋂ T(v) .

The activity set T(e) of a node/link e is usually described as a sequence of activity time intervals ([si,fi))i ∈ 1:k, where si is the starting time and fi is the finishing time.

We denote a network consisting of links and nodes active in the time t ∈ T by N(t) and call it the (network) time slice or footprint of t. Let T' ⊆ T (for example, a time interval). The notion of a time slice is extended to T' by

N(T') = ⋃t∈T' N(t) .

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tq/ug/intro.txt · Last modified: 2016/04/27 18:38 by vlado
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