The Neolithic agriculture revolution made fundamental changes in the organization of human societies. Compared to hunter-gatherer societies, even fairly crude slash-and-burn agriculture is an extremely efficient method of obtaining food. Agriculture intensifies food production for a given land area allowing for substantial increases in population density. Agriculture also favours fixed locations, as opposed to the necessary mobility of nomadic and hunter-gatherer means of obtaining food. The combination of population density and fixed locales lead to urbanisation and increasingly complex political structures. Irrigation, as developed in Mesopotamia and Egypt, in particular, requires large scale and long term cooperation among large groups of people.
Even more important, the relative efficiency of agriculture food production results in an economic surplus, i.e. no longer are all the people in the community engaged primarily in subsistence level food gathering. This allows for some specialization of labour, and the development of crafts -- e.g. potters who can trade pots for food -- leading to technological innovation.
Political structures are often influenced by the way the people live in country. For example, Indian land is mostly agricultural so the society have developed into agriculturian society, which in turn has maintained the political structure pertaining to agriculture. Green revolution has drastically changed the political system.
But if we talk of developed countries like America then we find that there political structure, by and large, is influenced by industries which in turn has provided highly improvised equipment for agriculture. Up and down has been witnessed by that countries just through the technology.
SO we can say that agriculture has deeply influenced the political structure.