▁set ▁inclusion ▁on ▁the ▁sub graph s ▁of ▁ ▁which ▁are ▁trees . ▁ ▁If ▁ ▁is ▁a ▁graph ▁and ▁ ▁a ▁maximal ▁tree , ▁then ▁the ▁fundamental ▁group ▁ ▁equals ▁the ▁free ▁group ▁generated ▁by ▁elements ▁, ▁where ▁the ▁ ▁correspond ▁bi ject ively ▁to ▁the ▁edges ▁of ▁; ▁in ▁fact , ▁ ▁is ▁hom ot opy ▁equivalent ▁to ▁a ▁w edge ▁sum ▁of ▁circles . ▁ ▁Form ing ▁the ▁topological ▁space ▁associated ▁to ▁a ▁graph ▁as ▁above ▁amounts ▁to ▁a ▁fun ctor ▁from ▁the ▁category ▁of ▁graphs ▁to ▁the ▁category ▁of ▁topological ▁spaces . ▁ ▁The ▁associated ▁topological ▁space ▁of ▁a ▁graph ▁is ▁connected ▁( with ▁respect ▁to ▁the ▁graph ▁topology ) ▁if ▁and ▁only ▁if ▁the ▁original ▁graph ▁is ▁connected . ▁ ▁Every ▁covering ▁space ▁project ing ▁to ▁a ▁graph ▁is ▁also ▁a ▁graph . ▁ ▁App lications ▁▁ ▁Using ▁the ▁above ▁properties ▁of ▁graphs , ▁one ▁can ▁prove ▁the ▁N iel sen – Sch re ier ▁theorem . ▁ ▁See ▁also ▁ ▁Top ological ▁graph ▁theory ▁ ▁References ▁▁ ▁Category : Top ological ▁spaces <0x0A> </s> ▁The o ▁van ▁de ▁V end el ▁( born ▁ 2 4 ▁October ▁ 1 9 8 0 ) ▁is ▁a ▁Dutch ▁Olympic ▁event ing ▁r ider . ▁He ▁competed ▁at ▁the ▁ 2 0 1 6 ▁Summer ▁Olympics ▁in ▁Rio ▁de ▁Janeiro ▁where ▁he ▁was ▁elimin ated ▁in ▁the ▁individual ▁and ▁finished ▁ 6 th ▁in ▁the ▁team ▁competition . ▁ ▁Van ▁de ▁V end el ▁also ▁participated ▁at ▁the ▁ 2