Monday, December 01, 2014

Cliques are nasty but Cliques are nastier

BILL: Today we will show that finding large cliques is likely a nasty problem

STUDENT: Yes! In my High School the Cliques were usually at most six people and they gossiped about everyone else. They were very nasty.

BILL: Um, yes, picture in your school that everyone is a node in a graph and that two nodes are connected if they are friends. In your school a clique of size 6 would be 6 people who all liked each other

STUDENT: Actually, the people in a clique secretly hated each other and sometimes belonged to other cliques that would gossip about people in the first clique.

BILL: We might need  the Hypergraph version to model your school.

Computer Scientists and Graph Theorists call a set of nodes that are all connected to each other a CLIQUE - pronounced CLEEK

High School Kids call a group of people who hang out together a CLIQUE- pronounced CLICK.

Which term came first? Why are they pronounced differently when they are quite related to each other? Do the members of a high school clique really hate each other?


  1. Clique is actually a french word that literally means 'click', as in clicking a mouse or a sharp sound. In french it would be pronounced CLEEK according to usual french language rules.

    I would guess the word came from french _before_ the medieval "Great Vowel Shift" in English, which caused tons of words like 'wipe', which used to be pronounced as WEEP, to be pronounced like WHY-PE. Thus the english word clique (group of mutually connected people) went from french CLEEK to english CLICK.

    However, since mathematics was predominantly not english until the 20th century, I would assume clique would be pronounced the french way when graph theory was invented.

  2. In my neck of the woods (Western Canada), we say CLEEK for both words. My guess is that it came from the social definition, but that the graph theorists who popularized it come from somewhere where the CLEEK pronunciation was standard.

  3. The high-school-kids usage dates to the early 1700s.

  4. Most people I know pronounce the graph theoretic clique as CLICK.

  5. The earliest reference I have for "cliques" in graphs is Luce and Perry's 1949 paper "A method of matrix analysis of group structure." I imagine this term was already part of the vernacular.

  6. Actually, the "High School Kids" sense is one of the senses of the French word which already existed in the 17th century, and is quite common nowadays in French. It has a pejorative sense of a group of people having bad intentions.

    I would guess that the etymology for the graph-theoretic sense comes from this French word since the sense is quite close. I've never looked for, nor found, a reference for this etymology though it seemed clear to me from the first time I was introduced to graph-theoretic cliques. And I was quite surprised to learn that the English word in the same since it sounded (and still sounds) like a French word to me.

  7. I don't see a good reason for pronouncing the two meanings of clique differently (I call them both "clicks") because they are really the exact same English word. It is not true, for instance, that the graph theory meaning was re-borrowed from French. The original paper that gave us the graph-theoretic terminology, Luce & Perry, Psychometrika 1949, was written in English and used graph theory to model the social-science kind of clique.

  8. I see your point about the origin of the graph-theoretic terminology, so my assumption was bad.

    My only other guess is that historically, there was (still is?) a strong proclivity among some English-speaking academics towards French origin roots and words as opposed to Anglo or Germanic origin roots and words, possibly a relic of the upper class Normans who ruled over lower class English over 800 years ago. It's possible that CLEEK simply sounded more 'formal and proper' (i.e. French) to highly educated people than CLICK.

  9. According to here:, both pronunciations are correct. But I agree that someone should pronounce the word the same regardless of whether they are talking about graphs or people.

    FWIW, I notice similar differences with the word "route." Is it pronounced like ROOT or like ROWT?

    1. I say "click" for high-school and "cleek" for graphs. I say "Root 66" and "What rowt are we taking?"

      Not logical at all...

    2. For me "root" for the noun, "rowt" for the verb. "The root we are taking is suboptimal! We should rerowt."

  10. This discussion makes no sense to non-native speakers. Must of us cannot distinguish the difference between CLICK and CLEEK when we hear it.