Citation networks can be obtained from bibliographic data bases such as Web of Science (Knowledge) and Scopus. In a citation network N = (V,L,T,P,W), its set of nodes V consists of selected works (papers, books, reports, patents, etc.). There exists an arc a(u,v) ∈ L iff the work u cites the work v. The time set T is usually an interval of years [yearfirst, yearlast] in which the works were published. The activity set of the work v, T(v), is the interval [pubyear(v), yearlast]; and the activity set of the arc a(u,v), T(a), can be set to the interval [pubyear(u), pubyear(u)] (instances approach) or to the interval [pubyear(u), yearlast] (cumulative approach). An example of a property p ∈ P is the number of pages or the number of authors. Other properties, such as work's authors and keywords, are usually represented as two-mode networks.
Project collaboration networks are usually based on some project data base such as Cordis. The set of nodes V consists of participating institutions. There is an edge e(u:v) ∈ L iff institutions u and v work(ed) on a joint project. The time set T is an interval of dates/days [dayfirst, daylast] in which the collaboration data were collected. T(v) = T and
T(e) = { [s,f] : there exists a project p such that u and v are partners on p; s is the start and f is the finish date of p }.
KEDS/WEIS networks are networks registering political events in critical regions in the world (Middle East, Balkans, and West Africa) on the basis of daily news. Originally they were collected by KEDS (Kansas Event Data System). Currently they are hosted by Parus Analytical Systems. The set of nodes V contains the involved actors (states, political groups, international organizations, etc.). The links are directed and are describing the events: ( date, actor1, actor2, action ) on a given date the actor1 made the action on the actor2. Different actions are determining different relations - we get a multi-relational network with a set of links partitioned by actions L = { Lact : act ∈ Actions }. The time set is determined by the observed period T = [dayfirst, daylast]. Since most of the actors are existing during all the observed period their node activity time sets are T(v) = T. Another option is to consider as their node activity time sets the period of their engagement in the region. The activity time set T(a) of an arc a(u,v) ∈ Lact contains all dates - intervals [day, day] - in which the actor u made an action act on the actor v.
910625 YUG YUGCRO 198 (WITHDRAW FROM) DECLARED INDEPENDENCE 910625 YUG SLO 198 (WITHDRAW FROM) DECLARED INDEPENDENCE 910625 YUGCRO YUG 081 (MAKE AGREEMENT) IS PLANS 910625 YUGCRO YUG 198 (WITHDRAW FROM) DECLARE INDEPENDENCE 910625 USA YUG 102 (URGE) REITERATED 910625 GER YUG 031 (MEET) TELEPHONED 910625 YUG GER 031 (MEET) TELEPHONED 910625 ITA YUG 031 (MEET) TELEPHONED 910625 YUG ITA 031 (MEET) TELEPHONED 910625 FRN SLO 121 (CRITICIZE) DISAPPROVED 910625 FRN YUGCRO 121 (CRITICIZE) DISAPPROVED 910626 SLO YUG 043 (RALLY) CELEBRATED 910626 YUGCRO SERMIL 223 (MIL ENGAGEMENT) KILLED 910626 USR YUGCRO 042 (ENDORSE) SOVIET SUPPORT FOR CROATIA 910626 USR SLO 042 (ENDORSE) SOVIET SUPPORT FOR CROATIA 910626 YUG SLO 182 (MILITARY DEMO) PUT ON ALERT 910626 YUG YUGCRO 223 (MIL ENGAGEMENT) KILLED 910626 SERMIL SLO 199 () COMBAT 910626 YUGGOV SLO 197 (CENSOR) OUTLAWED 910626 YUGGOV YUGCRO 197 (CENSOR) OUTLAWED 910626 YUGGOV SLO 210 (SEIZE) SEIZE 910626 AUL YUGCRO 022 (PESSIMIST COMMENT) SAID NOT 910626 USAGOV YUG 022 (PESSIMIST COMMENT) SAID NOT 910626 USA YUG 112 (REFUSE) OPPOSED 910626 USA EUR 160 (WARN) WARNED 910626 UNK YUG 094 (CALL FOR) CALLED ON 910626 NTH EEC 022 (PESSIMIST COMMENT) SAID NOT 910626 GERGOV YUG 102 (URGE) URGED 910627 SLO SERMIL 223 (MIL ENGAGEMENT) FIGHTING ERUPTED 910627 SLO SERMIL 223 (MIL ENGAGEMENT) SHOT 910627 SERMIL SLO 031 (MEET) SENT 910627 SLO SERMIL 121 (CRITICIZE) SLOVENIA SAID YUGOSLAV SOLDIER KILLED 910627 USR EUR 042 (ENDORSE) EXPRESSED SUPPORT 910627 SERMIL SLO 031 (MEET) SENDING 910627 SERMIL SLO 023 (NEUTRAL COMMENT) SAID 910627 YUG BAL 092 (ASK POLICY AID) SEEK INDEPENDENCE 910627 USA YUG 198 (WITHDRAW FROM) DECLARED INDEPENDENCE 910627 USA YUG 023 (NEUTRAL COMMENT) SAID
Part of the Weis encoded events file about Balkans.
Another possibility is to base the description on a single relation network and store the information about the action act as a structured value in a triple (day, day+1, value) (see Description).
value = [(act1, count1), (act2, count2), … ,(actk, countk) ]
and introduce an appropriate semiring over such values.
There are many other examples of temporal networks such as: genealogies,
contact networks, networks of phone calls, transportation (planes, trains, buses) time tables, etc.