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Mountaineering is a sport of contrary forces: teamwork plays a large role inmental fortitude and skills, but the actual act of climbing, and indeedsurvival, is largely individualistic. This work studies the effects of thestructure and topology of relationships within climbers on the level ofcooperation and success. It does so using simplicial complexes, whererelationships between climbers are captured through simplexes that correspondto joint previous expeditions with dimension given by the number of climbersminus one and weight given by the number of occurrences of the simplex. First,this analysis establishes the importance of relationships and shows thatchances of failure to summit reduce drastically when climbing with repeatpartners. From a climber-centric perspective, climbers that belong to simplexeswith large dimension were more likely to be successful, across experiencelevels. From an expedition-centric perspective, the distribution ofrelationships within a group is explored to identify collective human behavior:from polarized to cooperative. Expeditions containing simplices with largedimension, and usually low weight, i.e., a large number of people had a smallnumber of previous joint expeditions, tended to be more cooperative, with morehomogeneity in success amongst climbers. On the other hand, the existence ofsmall, usually strong, subgroups lead to a polarized style where climbers thatwere not a part of the subgroup were less likely to succeed. Lastly, this workexamines the effects of individual features and expedition-wide factors thatmay play different roles in individualistic and cooperative expeditions.Centrality indicates that individual traits of youth and oxygen use whileascending are strong drivers of success. Of expedition-wide factors, theexpedition size and number of expedition days are found to be stronglycorrelated with success rate.

The collective vs individual nature of mountaineering: a network and simplicial approach