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| - Atomic Walk Counts of Negative Order
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| - Atomic walk counts (awc's) of order k (k ≥ 1) are the number of all possible walks of length k which startat a specified vertex (atom) i and end at any vertex j separated by m (0 ≤ m ≤ k) edges from vertex i. Thesum of atomic walk counts of order k is the molecular walk count (mwc) of order k. The concept of atomicand molecular walk counts was extended to zero and negative orders by using a backward algorithm basedon the usual procedure used to obtain the values of mwc's. The procedure can also be used in cases inwhich the adjacency matrix A related to the actual structure is singular and therefore A-1 does not exist.awc's and mwc's of negative order may assume noninteger and even negative values. If matrix A is singular,atomic walk counts of zero order may not be equal to one.
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