A "walk" within a graph is usually defined for simple graphs, multigraphs or
even pseudographs as "alternating sequence of vertices and edges x0 , e1 ,
x1 , e2 , ... , e(l) , x(l) where e(i) = x(i-1)x(i), 0*Bollobas] p. 4. This definition requires the edges to connect two
vertices at most (loops are also allowed: if e(i) is a loop, then
x(i-1) = x(i)). For hypergraphs containing hyperedges (i.e. edges connecting
more than two vertices), however, a more general definition is needed. Two
approaches for a definition applicable for arbitrary hypergraphs are used in
the literature: "walks on the vertex level" and "walks on the edge level"
(see Aksoy, Joslyn, Marrero, Praggastis, Purvine: "Hypernetwork science via
high-order hypergraph walks", June 2020,
https://doi.org/10.1140/epjds/s13688-020-00231-0):
*

"walks on the edge level": For a positive integer s, an s-walk of length k between hyperedges f and g is a sequence of hyperedges, f=e(0), e(1), ... , e(k)=g, where for j=1, ... , k, e(j-1) =/= e(j) and e(j-1) and e(j) have at least s vertices in common (according to Aksoy et al.).

"walks on the vertex level": For a positive integer s, an s-walk of length k between vertices a and b is a sequence of vertices, a=v(0), v(1), ... , v(k)=b, where for j=1, ... , k, v(j-1) and v(j) are connected by at least s edges (analogous to Aksoy et al.).

There are two imperfections for the definition for "walks on the edge level": one is that a walk of length 1 consists of two edges (or a walk of length 0 consists of one edge), whereas a walk of length 1 on the vertex level consists of two vertices and one edge (or a walk of length 0 consists of one vertex and no edge). The other is that edges, especially loops, can be traversed only once (and not repeatedly) because of the condition e(j-1) =/= e(j). The latter is avoided in the definition for , see df-ewlks. To be compatible with the (usual) definition of walks for pseudographs, walks also suitable for arbitrary hypergraphs are defined "on the vertex level" in the following as , see df-wlks, restricting s to 1. wlk1ewlk shows that such a 1-walk "on the vertex level" induces a 1-walk "on the edge level".

- cewlks
- cwlks
- cwlkson
- df-ewlks
- df-wlks
- df-wlkson
- ewlksfval
- isewlk
- ewlkprop
- ewlkinedg
- ewlkle
- upgrewlkle2
- wkslem1
- wkslem2
- wksfval
- iswlk
- wlkprop
- wlkv
- iswlkg
- wlkf
- wlkcl
- wlkp
- wlkpwrd
- wlklenvp1
- wksv
- wlkn0
- wlklenvm1
- ifpsnprss
- wlkvtxeledg
- wlkvtxiedg
- relwlk
- wlkvv
- wlkop
- wlkcpr
- wlk2f
- wlkcomp
- wlkcompim
- wlkelwrd
- wlkeq
- edginwlk
- upgredginwlk
- iedginwlk
- wlkl1loop
- wlk1walk
- wlk1ewlk
- upgriswlk
- upgrwlkedg
- upgrwlkcompim
- wlkvtxedg
- upgrwlkvtxedg
- uspgr2wlkeq
- uspgr2wlkeq2
- uspgr2wlkeqi
- umgrwlknloop
- wlkRes
- wlkv0
- g0wlk0
- 0wlk0
- wlk0prc
- wlklenvclwlk
- wlklenvclwlkOLD
- wlkson
- iswlkon
- wlkonprop
- wlkpvtx
- wlkepvtx
- wlkoniswlk
- wlkonwlk
- wlkonwlk1l
- wlksoneq1eq2
- wlkonl1iedg
- wlkon2n0
- 2wlklem
- upgr2wlk
- wlkreslem
- wlkres
- redwlklem
- redwlk
- wlkp1lem1
- wlkp1lem2
- wlkp1lem3
- wlkp1lem4
- wlkp1lem5
- wlkp1lem6
- wlkp1lem7
- wlkp1lem8
- wlkp1
- wlkdlem1
- wlkdlem2
- wlkdlem3
- wlkdlem4
- wlkd