There are intermolecular forces of attraction that act between between molecules but these are not fibers.
Molecules are formed from atoms as the formation of the molecule results in a decrease in total energy. Atoms in molecules can have ionic bonds or covalent bonds.
The main forces of attraction between molecules are van der Walls bonds and hydrogen bonds.
Hydrogen bonds are due to hydrogen atoms retaining a small amount of charge when they react with atoms like oxygen, fluorine, chlorine, etc. The positive charge on the hydrogen atoms attracts the negatively charged atoms of other similar molecules. Hydrogen bonds are what make the boiling point of water very high compared to other liquids with similar molecular mass.
van der Walls bonding between molecules of substances in the liquid phase is due to a difference in polarity between different atoms that make up the molecule. Even molecules that have atoms linked with covalent bonds can have intermolecular van der Wall forces of attraction.