  Mountaineering is a sport of contrary forces: teamwork plays a large role in
mental fortitude and skills, but the actual act of climbing, and indeed
survival, is largely individualistic. This work studies the effects of the
structure and topology of relationships within climbers on the level of
cooperation and success. It does so using simplicial complexes, where
relationships between climbers are captured through simplexes that correspond
to joint previous expeditions with dimension given by the number of climbers
minus one and weight given by the number of occurrences of the simplex. First,
this analysis establishes the importance of relationships and shows that
chances of failure to summit reduce drastically when climbing with repeat
partners. From a climber-centric perspective, climbers that belong to simplexes
with large dimension were more likely to be successful, across experience
levels. From an expedition-centric perspective, the distribution of
relationships within a group is explored to identify collective human behavior:
from polarized to cooperative. Expeditions containing simplices with large
dimension, and usually low weight, i.e., a large number of people had a small
number of previous joint expeditions, tended to be more cooperative, with more
homogeneity in success amongst climbers. On the other hand, the existence of
small, usually strong, subgroups lead to a polarized style where climbers that
were not a part of the subgroup were less likely to succeed. Lastly, this work
examines the effects of individual features and expedition-wide factors that
may play different roles in individualistic and cooperative expeditions.
Centrality indicates that individual traits of youth and oxygen use while
ascending are strong drivers of success. Of expedition-wide factors, the
expedition size and number of expedition days are found to be strongly
correlated with success rate.
