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Rhizome is a philosophical concept developed by Gilles Deleuze and Félix Guattari in their Capitalism and Schizophrenia (1972–1980) project. It is what Deleuze calls an "image of thought", based on the botanical rhizome, that apprehends multiplicities.
Rhizome as a mode of knowledge and model for society 
Gilles Deleuze and Félix Guattari use the term "rhizome" and "rhizomatic" to describe theory and research that allows for multiple, non-hierarchical entry and exit points in data representation and interpretation. In A Thousand Plateaus, they oppose it to an arborescent conception of knowledge, which works with dualist categories and binary choices. A rhizome works with planar and trans-species connections, while an arborescent model works with vertical and linear connections. Their use of the "orchid and the wasp" is taken from the biological concept of mutualism, in which two different species interact together to form a multiplicity (i.e. a unity that is multiple in itself). Horizontal gene transfer would also be a good illustration.
As a model for culture, the rhizome resists the organizational structure of the root-tree system which charts causality along chronological lines and looks for the original source of "things" and looks towards the pinnacle or conclusion of those "things." A rhizome, on the other hand, is characterized by "ceaselessly established connections between semiotic chains, organizations of power, and circumstances relative to the arts, sciences, and social struggles." The rhizome presents history and culture as a map or wide array of attractions and influences with no specific origin or genesis, for a "rhizome has no beginning or end; it is always in the middle, between things, interbeing, intermezzo." The planar movement of the rhizome resists chronology and organization, instead favoring a nomadic system of growth and propagation. In this model, culture spreads like the surface of a body of water, spreading towards available spaces or trickling downwards towards new spaces through fissures and gaps, eroding what is in its way. The surface can be interrupted and moved, but these disturbances leave no trace, as the water is charged with pressure and potential to always seek its equilibrium, and thereby establish smooth space.
Principles of the rhizome 
Deleuze and Guattari introduce A Thousand Plateaus by outlining the concept of the rhizome (quoted from A Thousand Plateaus):
- 1 and 2: Principles of connection and heterogeneity: any point of a rhizome can be connected to anything other, and must be
- 3. Principle of multiplicity: only when the multiple is effectively treated as a substantive, "multiplicity" that it ceases to have any relation to the One
- 4. Principle of asignifying rupture: a rhizome may be broken, but it will start up again on one of its old lines, or on new lines
- 5 and 6: Principle of cartography and decalcomania: a rhizome is not amenable to any structural or generative model; it is a "map and not a tracing"
See also 
- Deleuze, Gilles and Félix Guattari. 1980. A Thousand Plateaus. Trans. Brian Massumi. London and New York: Continuum, 2004. Vol. 2 of Capitalism and Schizophrenia. 2 vols. 1972-1980. Trans. of Mille Plateaux. Paris: Les Editions de Minuit. ISBN 0-8264-7694-5.
- Guattari, Félix. 1995. Chaosophy. Ed. Sylvère Lotringer. Semiotext(e) Foreign Agents Ser. New York: Semiotext(e). ISBN 1-57027-019-8.
- ---. 1996. Soft Subversions. Ed. Sylvère Lotringer. Trans. David L. Sweet and Chet Wiener. Semiotext(e) Foreign Agents Ser. New York: Semiotext(e). ISBN 1-57027-030-9.
- Rhizomes" – Cultural Studies Online Journal.
- Power of Networks" – RSA Animate video on the "Power of Networks" by Manuel Lima (juxtaposes the tree vs. network approach).