This paper addresses the collision-free consensus problem in a network of agents with single-integrator dynamics. Distributed algorithms with local interactions are proposed to achieve consensus while guaranteeing collision-free among agents during the evolution of the multi-agent networks. The novelty of the proposed algorithms lies in the definition of neighbors for each agent, which is different from the usual sense that neighbors are selected by the distance between agents in the state space. In the proposed strategies, the neighbor set for each agent is determined by the distance or difference between agents in the index space after ordering and labeling all agents according to certain ordering rules including weighted order and lexicographic order. The consensus analysis of the proposed algorithms is presented with some existing results on algebraic graph theory and matrix analysis. Meanwhile, by realizing the relations between order preservation and collision-free, a systematic analysis framework on order preservation and hence collision-free for agents in arbitrary dimension is provided based on tools from monotone systems theory. Illustrated numerical examples are presented to validate the effectiveness of the proposed strategies. (C) 2015 Elsevier Ltd. All rights reserved.